The dependence of bound states in the continuum(BICs) on C2 and C6 rotational symmetry in photonic crystal plates has been extensively studied numerically. However, a rigorous theoretical analysis process is lacking, and there is a lack of studies on C4 rotational symmetries. In view of this, a theory of systematic analysis of the dependence of BICs on all rotational symmetries was constructed, and the case of C4 rotational symmetry was mainly studied. Firstly, by analyzing the characteristic solutions of Maxwell's equations with rotationally symmetric structure, the problem of the existence of BICs was transformed into the question of whether the eigenvalue of the rotation matrix was the same as the solution of a simple algebraic equation. Secondly, the conditions for the existence of BICs in C4 rotationally symmetric structures were given. Then, it was proved that the BICs still existed when C4 rotation symmetry was destroyed and C2 rotatory symmetry was maintained. Finally, the finite element software, FreeFEM, was used to do a lot of numerical verifications. The above theory can be applied to all cases of rotational symmetries, revealing the importance of rotational symmetry for the existence of BICs. The dependence between high-order and low-order rotational symmetries was revealed providing theoretical guidance for applying BICs.