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The two-component formulation of quantum electrodynamics with fundamentalmass is studied. We review and update the prediction of the primordialexistence of lepton magnetic moment in framework of two component formulationof the Maximal Mass Model containing a limiting mass $M$, which is consideredas new universal physical constant. As it well known in the Dirac theoryso-called gyromagnetic factor $g=2$. Quantum electrodynamics together withelectro-weak theory and hadronic contributions predicts deviations from Dirac'svalue. It is very important that all these effects \textbf{slightly increasethe $g$-value}. But in our model we have any decreasing of this quantity$g=2\sqrt{1-m^2/M^2}$, where $m$ - is a lepton mass. The most intriguingprediction of new approach is the absolute value of this deviation increaseswith growth of a lepton mass. In this connection the direct experimentalmeasurements of $\tau$ - lepton anomalous magnetic moment $a_\tau = (g - 2)/2$gain in extraordinary importance. The most stringent limit $-0.052 < a_{\tau} <0.013$ at 95% confidence level, was set by the {\small DELPHI}\cite{delphi}collaboration. The authors also quote their result in the form of central valueand error $ a_\tau = - 0.018(17).$ To pay attention that the sign of $a_\tau$is the negative and now we can speak about a qualitative agreement with ourpredictions.

The Maximal Mass Model and Lepton Magnetic Moment