Abstract: Dirac derived the equation of relativistic quantum mechanics by requiring it be linear and satisfy the relativistic mass-energy relation; to this end, he introduced the coefficients in 4×4 matrices, and, correspondingly, the wavefunction assumes a 4-component form. In the context of Dirac equation, electron spin is attributed to the relativistic effect, and the concept of positron was eventually proposed from the interpretation to the solution. However, the choice of a 4 × 4 matrix form—along with its specific representation—for the coefficients in the equation lacks fundamental justification; furthermore, interpreting the wavefunction as a 4-component entity is also unreasonable. In this paper, by introducing four sets of independent creation and annihilation operators (b_k, b_k⁺), k = 0, 1, 2, 3 we derive a novel representation of the Dirac equation. This approach not only circumvents the question of why 4×4 matrices were chosen for the coefficients, but also resolves the issue of the non-equivalence of the matrix coefficients present in Dirac's original equation. The relativistic mass-energy equation requires anticommutative creation and annihilation operators (b_k, b_k⁺, this directly determines that the “spin”thereby introduced is a two-valued internal degree of freedom, which explains why Dirac theory encompasses only the case of S = 1/2.Under this new formalism, the external part of angular momentum and“spin”assume identical forms; furthermore, both the angular momentum and the Hamiltonian exhibit a coupling between the external degree of freedom, which satisfies commutation relation, and internal degree of freedom, which satisfies anticommutation relation. This new formulation of the Dirac equation eliminates the need for 4×4 matrix representations—a feature that, at the very least, promises to simplify subsequent calculations in quantum field theory. Furthermore, we note that during the period from 1926 to 1930, Dirac and Schrödinger possessed a profound and accurate understanding of concepts within quantum theory—such as complex conjugation, charge conjugation, and internal degrees of freedom—as well as the interconnections among them. The current paper also briefly discusses issues pertinent to the interpretation of relativistic quantum mechanical equation—specifically, complex conjugation, charge conjugation, internal degree of freedom and their coupling with dynamical variables, and the algebraic structures that the elements of the Dirac equation must obey—with the aim of facilitating a correct understanding of relativistic quantum mechanics.