  We present Lagrangian which implies both necessary constraints and dynamical
equations for position and spin of relativistic spin one-half particle. The
model is consistent for any value of magnetic moment $\mu$ and for arbitrary
electromagnetic background. Our equations coincide with those of Frenkel in the
approximation in which the latter have been obtained by Frenkel. Transition
from approximate to exact equations yields two structural modifications of the
theory. First, Frenkel condition on spin-tensor turns into the Pirani
condition. Second, canonical momentum is no more proportional to velocity. Due
to this, even when $\mu=1$ (Frenkel case), the complete and approximate
equations predict different behavior of particle. The difference between
momentum and velocity means extra contribution into spin-orbit interaction. To
estimate the contribution, we found exact solution to complete equations for
the case of uniform magnetic field. While Frenkel electron moves around the
circle, our particle experiences magnetic {\it Zitterbewegung}, that is
oscillates in the direction of magnetic field with amplitude of order of
Compton wavelength for the fast particle. Besides, the particle has dipole
electric moment.
