In this present communication we provide a new derivation of the Dirac dual structure by employing a different approach from the originally proposed one. Following a general and rigorous mathematical process to compute the dual structure, we investigate if is possible to break the existing "rigidity" in its primordial formulation. For this task, firstly, we look towards to understand the core of the Dirac spinors construction (Dirac P. A. M., Proc. R. Soc. Lond. A, 117 (1928) 610). and then, we suggest to build an alternative dual structure for the Dirac spinor, which preserves an invariant norm under any transformation. Finally, we verify if the prominent physical content is maintained or if it is affected by such construction.