  We employ the conformal bootstrap to re-examine the problem of finding the
critical behavior of four-Fermion theory at its strong coupling fixed point.
Existence of a solution of the bootstrap equations indicates self-consistency
of the assumption that, in space-time dimensions less than four, the
renormalization group flow of the coupling constant of a four-Fermion
interaction has a nontrivial fixed point which is generally out of the
perturbative regime. We exploit the hypothesis of conformal invariance at this
fixed point to reduce the set of the Schwinger-Dyson bootstrap equations for
four-Fermion theory to three equations which determine the scale dimension of
the Fermion field $\psi$, the scale dimension of the composite field
$\bar{\psi}\psi$ and the critical value of the Yukawa coupling constant. We
solve the equations assuming this critical value to be small. We show that this
solution recovers the fixed point for the four-fermion interaction with
$N$-component fermions in the limit of large $N$ at (Euclidean) dimensions $d$
between two and four. We perform a detailed analysis of the $1/N$-expansion in
$d=3$ and demonstrate full agreement with the conformal bootstrap. We argue
that this is a useful starting point for more sophisticated computations of the
critical indices.
