  We propose gauge parameterization of the three-dimensional $n$-field using
orthogonal SO(3)-matrix which, in turn, is defined by a field taking values in
the Lie algebra so(3) (rotational-angle field). The rotational-angle field has
an additional degree of freedom, which corresponds to the gauge degree of
freedom of rotations around the $n$-field. As a result, we obtain a gauge model
with local SO(2)=U(1) symmetry that does not contain a U(1) gauge field.
