Abstract: 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: \mathop \max \limits_S_kS_k^H = I_n,W_kW_k^H = I_t,V_kV_k^H = I_m \left| \texttr\left( cI_m \pm \prod\limits_k = 1^2 \Gamma _k S_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 \in \mathbfC, \texttr( \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.