  We consider a natural form of unified theory of gravity and electromagnetism
which was somehow missed at the time of intense search for such an unification,
and was noticed only in 1978 but remained quite unknown. The basic idea of this
unification is to use the metric and non-symmetric connection as independent
variables, which generalizes the so-called Palatini formalism. The certain
components of connection in the appearing theory can be naturally identified
with electromagnetic potential, and with the proper choice of action the
Einstein-Maxwell equations are reproducing. In this paper we compare such an
approach with the known ideas of unification. Also we propose the more
consistent way of including matter (in the form of classical particles) in the
theory and briefly discuss the perspectives of further development of this
approach.
