In 1992, Gregory gave a rigorous proof about thedecomposed form when stress is anti-symmetrical about the mid-plane. Hisproof is dependent on his previous work, i.e., the Papkovich-Fadleeigenfunction expansion of bi-orthogonal functions. In this paper, wegeneralize isotropic elastic plate to transversely isotropic elastic plate.And give the decomposed theorem of the transversely isotropic elastic plate,ie. the general state of stress in the plate can be decomposed three parts:the interior state, the shear state and the transcendental state. Our proofis concise and direct and independent of the Papkovich-Fadle eigenfunctionexpansion of bi-orthogonal functions.