Summary: ``The matrix optimization problem with unitary constraints is widely used in the fields of data control theory and electronic structure calculation. In this paper, we consider a class of unitary constrained matrix trace maximization problems as follows: $$ \max_{S_kS_k^H=I_n,W_kW_k^H=I_t,V_kV_K^H=I_m}\left|{\rm tr}\left(cI_m\pm\prod_{k=1}^2\Gamma_kS_k\Delta_kW_kH_kV_k\right)\right|, $$ where $\Gamma_k$, $\Delta_k$, $H_k$ are $m\times n$, $n\times t$, $t\times m$ complex diagonal matrices respectively, $k=1,2$. $c=\bold C$, ${\rm tr}(\cdot)$ denotes the matrix trace function, $I_m$ is the $m\times m$ identity matrix. On the basis of predecessor research result, it is considered that the coefficients are complex and the studied matrix is of different dimensions. Finally, numerical experiments are given to verify the effectiveness of the results.''