In this paper we present analytic solutions of a class of matrix minimization model with unitary constraints as follows:$$\mathop{\rm min}_{U_k\in {\rm U}_n, W_k\in {\rm U}_t, V_k\in {\rm U}_m} \ | {\rm det}(cI_m\pm \prod\limits_{k=1}^s A_k U_k B_k W_k C_k V)|$$ $$\mathop{\rm min}_{U_k\in {\rm U}_n, W_k\in {\rm U}_t, V_k\in {\rm U}_m} |{\rm tr}(cI_m \pm \prod^s_{k=1}A_k U_K B_k W_k C_k V)| $$ where $A_k\in C^{m\times n}$, $B_k\in C^{n\times t}$, $C_k\in C^{t\times m}$, $C^{m\times n}$ denotes $m\times n$ complex matrix set, and $c$ is a complex number, $I_m$ denotes the $m$-order identity matrix, det$(\cdot)$ and tr$(\cdot)$ denote matrix determinant and trace function, respectively. The proposed results improve some existing ones in Xu (2019) [1]. Numerical examples are given to verify the validity of the theoretical results.