Legal Question in Business Law in Texas

Generally, yes. In Texas most employment is "at will". So at the will of the employer an employee may be fired (so long as there isn�t an employment contract).

The major exception would be if you are firing a person BECAUSE of an illegal reason (ex. race, religion, gender, etc.). You should also make reasonable accommodations to a disabled employee.

Ultimately, if you have a good reason to fire someone you will be safe. Also remember that if you have multiple employees, you shouldn't let one employee get away with the very thing that you fire another employee for (doing so may make it appear that your are firing for an alternate-illegal reason).

You should consult an attorney for a more in depth analysis to your specific situation.

Good Luck!