How to Handle an Employee Who Tells Obvious Lies

My husband and I own a small business. We typically have no more than 2 employees at any given time. We recently had to terminate an employee because we could no longer trust her. On several occasions, she has told lies to justify some very major mistakes she has made on the job. In the 2 most serious instances we had complete and unquestionable proof of her lies, but when confronted she would still insist that somehow our proof must be wrong and that she is certain she is telling the truth.

She seems to have no regard for how her actions might affect the business, and in fact, seems shocked and surprised that she is even being reprimanded for the screw-ups let alone the lying that accompanied them. She became extremely defensive when told that we did not believe her. She was employed for less than 3 weeks and we were well within our rights to terminate her at this time.

However, since she appears to have a serious personality disorder, we feel it is likely that she will continue to be a "problem" for us. She has not returned her keys as she promised, and is threatening us in attempting to get her final paycheck prior to the end of the payroll period. We have fears that she may attempt to sabotage our business in some way to get back at us for what she evidently views as a wrongful termination.

How should we handle this situation? We would like to disentangle ourselves from this person as completely as possible without provoking her further. Since she appears to be living in a separate reality from the rest of us, we are at a loss! Please help!