An exact renormalization group equation is derived for the free energy
of matrix models. The renormalization group equation turns out to be
nonlinear for matrix models, as opposed to vector models, where it is
linear. An algorithm for determining the critical coupling constant an
d the critical exponent is obtained. As concrete examples, one-matrix
models with one and two coupling constants are analyzed and the exact
values of the critical coupling constant and the associated critical e
xponent are found.