| A double sine Fourier series with supplementary terms function is adopted to investigate the cracked rectangular plate. The cracked plate is decomposed into several sub-domains and simplified function for each sub-domain is derived. For each specific function, the boundary conditions and the physical meanings for constants in original function are considered. Equation system, which contains governing equations, remaining boundary conditions, compatibility conditions for public boundary and the proposed equilibrium condition for public free corner in this paper, is converted to generalized eigenvalue problem to compute the non-dimensional frequencies. A sample is calculated and the results in this paper are close to published datas, which verified the correctness of derivition. Moreover, the validity of the proposed equilibrium condition for public free corner is proved. The adopted function, whose canstants contains certain physical meanings, could conveniently investigates layered rectangular plate with aribitrary boundary condition. Therefore, the method in this paper could unify the solution and simplify the approach for the study of rectangular plate.