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The question of how does the Dirac equation depend on the choice of the$\gamma$ matrices has partially been addressed and explored in the literature.In this paper we focus on this question by considering a general form of$\gamma$ matrices, and call the resulting spin $\frac{1}{2}$ fermions as\textit{intermediate fermion species} (IFS). By inspecting the properties ofIFS, we find that all species transform to each other by a $SO(3)$ similaritytransformation in the space of parameters, that are the entities of the$\gamma$ matrices. Many properties, like eigenvalue problem and boost aretested for IFS. We find also sub-representations that generate Majoranafermions, which is isomorphism to $U(1)$ group.

The intermediate fermionic species created by $SO(3)$ rotation in the representation of the Dirac equation