  We calculate the in-plane magnetoresistance $\Delta\rho_{xx}/\rho_{xx}$ of
YBa$_2$Cu$_3$O$_7$ in a magnetic field applied perpendicular to the $CuO_2$
planes for the ``cold spots'' model. In this model, the electron relaxation
time $\tau_2\propto1/T^2$ at small regions on the Fermi surface near the
Brillouin zone diagonals is much longer than the relaxation time
$\tau_1\propto1/T$ at the rest of the Fermi surface ($T$ is temperature). In
qualitative agreement with the experiment, we find that Kohler's rule is
strongly violated, but the ratio $\Delta\rho_{xx}/\rho_{xx}\tan^2\theta_H$,
where $\tan\theta_H$ is the Hall angle, is approximately
temperature-independent. We find the ratio is about 5.5, which is of the same
order of magnitude as in the experiment.
