The fourth Painlevé equation PIV is known to have symmetry of the affine Weyl group of type with respect to the Bäcklund transformations. We introduce a new representation of PIV, called the symmetric form, by taking the three fundamental invariant divisors as the dependent variables. A complete description of the symmetry of PIV is given in terms of this representation. Through the symmetric form, it turns out that PIV is obtained as a similarity reduction of the 3-reduced modified KP hierarchy. It is proved in particular that the special polynomials for rational solutions PIV, called Okamoto polynomials, are expressible in terms of the 3-reduced Schur functions.