  A proposal is made for reducing the solution of the N-particle
Lippmann-Schwinger equation to that of smaller sets of particles. This consists
of first writing the N-particle equation in terms of all possible
$N/2$-particle Lippmann-Schwinger equations. (If N is odd this needs a minor
modification.) The second step requires a decoupling of the resolvents for the
fewer particle systems so that each can be solved separately. This
generalization of the Faddeev approach deals only with connected kernels and
the homogeneous solution reproduces the N-particle Schr\"odinger equation. For
four particles the proposed method involves only a $3\times3$ matrix whereas
other approaches typically require the solution of at least a $7\times7$ matrix
equation.
