  A compact graph rule for the effective action $\Gamma[\phi]$ of a local
composite operator is given in this paper. This long-standing problem of
obtaining $\Gamma[\phi]$ in this case is solved directly without using the
auxiliary field. The rule is first deduced with help of the inversion method,
which is a technique for making the Legendre transformation perturbatively. It
is then proved by using a topological relation and also by the sum-up rule.
Explicitly derived are the rules for the effective action of $\langle
\varphi(x)^2 \rangle$ in the $\varphi^4$ theory, of the number density $\langle
n_{{\bf r}\sigma} \rangle$ in the itinerant electron model, and of the gauge
invariant operator $\langle \bar{\psi}\gamma^\mu\psi \rangle$ in QED.
