  Using the random matrix theory (RMT) approach, we calculated the weak
localization correction to the shot noise power in a chaotic cavity as a
function of magnetic field and spin-orbit coupling. We found a remarkably
simple relation between the weak localization correction to the conductance and
to the shot noise power, that depends only on the channel number asymmetry of
the cavity. In the special case of an orthogonal-unitary crossover, our result
coincides with the prediction of Braun et. al [J. Phys. A: Math. Gen. {\bf 39},
L159-L165 (2006)], illustrating the equivalence of the semiclassical method to
RMT.
