In this paper we will present a new method to compute the determinants of a 4 × 4 matrix. This new method gives the same result as other methods, used before, but it is more suitable. The advantage of this method comparing to other known methods is quick computation, so it creates an easy scheme to compute the determinants of a 4 × 4 matrix. The results achieved with this method are based on the Sarru’s rule, used for computing the third order determinants.