Abstract: To address the logical inconsistency arising from the simultaneous use of the straight normal assumption ( \varepsilon _\mathrmz=0 ) and the neglect of transverse normal stress ( \sigma _\mathrmz=0 ) in the classical Kirchhoff thin plate theory within the framework of elasticity, this paper presents a rigorous derivation that retains only the straight normal hypothesis. Through algebraic manipulation, the stress field in the thin plate, including a non-zero \sigma _\mathrmz term, is derived. It is demonstrated that after internal force integration, the resulting equivalent equilibrium equations are fully consistent with the classical theory. Furthermore, order-of-magnitude analysis confirms that for thin plate structures, \sigma _\mathrmz is a higher-order small quantity, and its neglect in the classical theory is asymptotically rational. This study resolves the logical circularity in the traditional derivation, providing a self-consistent and rigorous mechanical foundation for thin plate theory and revealing its inherent consistency as an approximate theory.