Recently, Hong-Jun Kim et al. introduced an improved process incapability index $C^*_{psk}$ by the transformation of the $C_{psk}{;}C^*_{psk}$. A simple transformation of $C_{psk}$, can be regard as a process incapability index, provides an uncontaminated separation between information concerning the process accuracy and precision while this kind of information separation is not available with the $C_{psk}$. By an identical conception, in this article a new process incapability index $C^*_{psk}$ for Non-Normal process can be proposed by the transformation of the process capability index $C^*_{psk}$. The motivation behind introduction of $C^*_{psk}$ is that process capability index $C^*_{psk}$ cannot give information of the process accuracy and precision. A significant result of this research that $C^*_{psk}$ for the case where the target value T is equal to the midpoint of the specification limits or not Is evaluated without respect to T. Accordingly, $C^*_({psk})$ will be propose a reasonable process incapability measure for Non-Normal process