  The magnetic translation group was introduced as a set of operators
T(R)=\exp[-iR.(p-eA/c)/\hbar]. However,these operators commute with the
Hamiltonian for an electron in a periodic potential and a uniform magnetic
field if the vector potential A (the gauge) is chosen in a symmetric way. It is
showed that a local gauge field A_R(r) on a crystal lattice leads to operators,
which commute with the Hamiltonian for any (global) gauge field A=A(r). Such
choice of the local gauge determines afactor system \omega(R,R')= T(R)T(R')
T(R+R')^{-1}, which depends on a global gauge only. Moreover, for any potential
A a commutator T(R)T(R')T(R)^{-1}T(R')^{-1} depends only on the magnetic field
and not on the gauge.
