  We consider the general form of the linear transformation for point rotation
coordinate frames. The frames have the rotation axis at every point. In the
transformation the frequency of one frame relative to another is not equivalent
to the reverse frequency. Using symmetry of the direct and reverse
transformation as well as symmetry of the frame coordinates we show that two
different type of the transformation are possible. The first type is a
generalization of the Lorentz transformation. This case can not be checked in
optical measurements. In contrast to that the second unusual type allows us to
observe consequences of the transformation in an optical experiment even though
the characteristic constant inherent in the transformation is less than
"nuclear time" of the order of 10^{-23} sec. We describe the experiment.
