  We propose a new representation of the fourth Painlev\'e equation in which
the $A^{(1)}_2$-symmetries become clearly visible. By means of this
representation, we clarify the internal relation between the fourth Painlev\'e
equation and the modified KP hierarchy. We obtain in particular a complete
description of the rational solutions of the fourth Painlev\'e equation in
terms of Schur functions. This implies that the so-called Okamoto polynomials,
which arise from the $\tau$-functions for rational solutions, are in fact
expressible by the 3-reduced Schur functions.
