The limitation of the occurrence of stick-slip vibration is explained which has been obtained analytically based on a 1-DOF system with Coulomb friction. The limitation is determined by two dimensionless parameters; one denotes the easiness for the occurrence of stick-slip vibration and the other is the damping ratio acting to suppress the vibration. A simple non-occurrence inequality of stick-slip vibration is proposed with two dimensionless parameters, which has both high accuracy and high usability.