  We formulate the conformal bootstrap approach to four--fermion theory at its
strong coupling fixed point in dimensions $2<d<4$. We present a solution of the
bootstrap equations in the five--vertex approximation. We show that the
bootstrap approach gives a particularly simple way to obtain next to leading
order corrections to critical exponents in the large $N$ expansion and present
the values of the anomalous dimensions of the fermion field $\psi$ and the
composite $\bar\psi\psi$ to order $1/N^2$.
