An analysis is presented of the possible existence of a second anomalous dipole moment of Dirac’s particle next to the angular one. It includes a discussion why, in spite of his own derivation, Dirac has denied its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading textbooks. A critical survey is given on the reasons of its reject, including the failure of attempts to measure and its perceived violation of the CPT theorem. Moreover, by reference from literature, the possible impact is discussed in the nuclear domain and in the gravitational domain if it would exist.