
628 So.2d 1224 (1993)
Helen Cormier CROOMS, Plaintiff-Appellant,
v.
LAFAYETTE PARISH GOVERNMENT; Parish of Lafayette Erroneously Referred to as Lafayette Parish Government, Defendant-Appellee.
No. 93-526.
Court of Appeal of Louisiana, Third Circuit.
December 8, 1993.
*1225 Jo Ann Nixon, Lafayette, for Helen Cormier Crooms.
Michael David Skinner, Lafayette, for Lafayette Parish Government, etc.
Steven Michael Jankower, Lafayette, for Parish of Lafayette.
Before DOUCET, YELVERTON and WOODARD, JJ.
WOODARD, Judge.
This is an appeal from a judgment sustaining defendant's peremptory exception of no cause of action and dismissing plaintiff's suit.

FACTS
Plaintiff, Helen Cormier Crooms, was employed by the Lafayette Parish Public Library as a desk clerk. Her duties included collecting fines for overdue books and tapes. On September 14, 1984, the director of the library, Ms. Sonya Branch, told plaintiff that she had reason to believe plaintiff had taken library fine money. She then asked her to tender her resignation. When plaintiff refused to resign, she was fired.
On September 14, 1990, plaintiff filed this lawsuit against the Parish of Lafayette, alleging that she was wrongfully discharged without just or legal cause. On December 8, 1992, defendant filed a peremptory exception of no cause of action.
The hearing on the exception was held December 10, 1992. Defendant argued that plaintiff was an at-will employee and the law does not provide a cause of action for wrongful discharge of an at-will employee. Plaintiff's attorney agreed that plaintiff was an at-will employee, but argued that she had a cause of action because the reason given for her discharge was untrue.
The trial court found that plaintiff did not have a cause of action and rendered judgment on December 29, 1992, sustaining defendant's peremptory exception and dismissing the lawsuit with prejudice. It is from this judgment that plaintiff appeals, asserting that the trial court erred in sustaining the exception of no cause of action.

LAW
The purpose of an exception of no cause of action is to determine the legal sufficiency of the petition, and it is triable on the face of the papers. All well pleaded facts in the petition and any annexed documents must be accepted as true. Kuebler v. Martin, *1226 578 So.2d 113 (La.1991). Plaintiff asserts that the trial court erred in sustaining defendant's exception because the pleadings state a cause of action for both wrongful discharge and defamation.

WRONGFUL DISCHARGE
Plaintiff's petition asserts that plaintiff was "wrongfully discharged from her position with the Lafayette Parish Library Main Branch Location without just or legal cause." However, plaintiff's petition does not allege that she was hired for a specific term of employment or that there is any specific statutory requirement or contractual agreement regulating the employment relationship of the parties. Thus, plaintiff is an at-will employee, as admitted at the hearing on the exception. In the absence of a specific contract or agreement establishing a fixed term of employment, an employer is at liberty to dismiss an employee at any time, for any reason, without incurring liability for wrongful discharge. La.C.C. art. 2747; Fontenot v. Manpower [Motivation], Educ., 594 So.2d 998 (La.App. 3 Cir.1992); Brodhead v. Board of Trustees, 588 So.2d 748 (La.App. 1 Cir.1991), writ denied, 590 So.2d 597 (La. 1992). Thus, the trial court did not err in finding that plaintiff had no cause of action for wrongful discharge.

DEFAMATION
The crux of plaintiff's argument on appeal is that her action is essentially one for defamation and that the petition states a cause of action for defamation. The pertinent paragraphs of plaintiff's petition state as follows:
8.
The defendant through its employee at the library accused the plaintiff of misappropriating these funds and asked for her resignation.
9.
When plaintiff refused to render her resignation, the defendant through their employee terminated her.
10.
The defendant did not at this time or at anytime subsequent to the discharge proved the plaintiff guilty of any wrong doing.
11.
Due to the nature of the accusation against the plaintiff this termination has reflected adversely on her character and has hindered employment opportunities available to her.
The essential elements for a claim for defamation are: (1) defamatory words; (2) publication, which is communication to a person other than the one alleging the action; (3) falsity; (4) malice, actual or implied; and (5) resulting injury. Gugliuzza v. K.C.M.C., Inc., 606 So.2d 790 (La.1992), Owens v. Jackson, 550 So.2d 359 (La.App. 3 Cir.1989). Words which impute a crime to another are defamatory per se, and proof of malice is not required. Cangelosi v. Schwegmann Bros., Etc., 390 So.2d 196 (La.1980), Martin v. Lincoln General Hosp., 588 So.2d 1329 (La.App. 2 Cir.1991), writ denied, 592 So.2d 1302 (La. 1992). Plaintiff's petition fails to allege anything indicating publication or communication of the defamatory words to anyone other than plaintiff. As a result, plaintiff's petition fails to state a cause of action for defamation. Thus, the trial court properly sustained defendant's peremptory exception of no cause of action.
However, we find that the trial court erred in dismissing plaintiff's suit without first giving her an opportunity to amend the petition. La.C.C.P. art. 934 provides:
When the grounds of the objection pleaded by the peremptory exception may be removed by amendment of the petition, the judgment sustaining the exception shall order such amendment within the delay allowed by the court. If the grounds of the objection cannot be so removed, or if plaintiff fails to comply with the order to amend, the action shall be dismissed.
*1227 Because plaintiff may be able to state a cause of action for defamation by amending her petition, we will reverse that portion of the trial court judgment dismissing the action with prejudice.
For the foregoing reasons, the judgment of the trial court sustaining defendant's peremptory exception of no cause of action is affirmed, but the dismissal of plaintiff's suit is reversed. The case is remanded to the trial court with instructions that the court order the plaintiff to amend her petition, if facts permit, within a reasonable period of time or else suffer dismissal of her suit. Costs of this appeal are assessed one-half to plaintiff and one-half to defendant.
AFFIRMED IN PART, REVERSED IN PART, AND REMANDED.
