Let $S;=;R[chi_{ij}mid1;{le};i;{le};m,;1;{le};j;{le};n]$ be the polynomial ring over a noetherian commutative ring R and $I_p$ be the determinantal ideal generated by the $p; imes;p$ minors of the generic matrix $(chi_{ij})(1{le}P{le}min(m,n))$. We describe a minimal free resolution of $S/I_{p}$, in the case m = n = p + 2 over $mathbb{Z}$.