In complex modules over real Clifford algebras of even dimension, fermionic variables, which are an analogue of the Witt basis, are introduced. Based on them, primitive idempotents are built which represent the equivalent Clifford vacua. It is shown that modules of algebras are decomposed into a direct sum of minimal left ideals, generated by these idempotents, and that fermionic variables can be considered as more fundamental mathematical objects than spinors.