In this paper, a geometric approach to the synthesis of a residual generator for fault detection and isolation (FDI) in bilinear systems is considered. A necessary and sufficient condition to solve the so-called fundamental problem of residual generation is presented. The proposed approach resorts to extensions of the notions of (C, A) invariant and unobservability subspaces, and it yields a constructive design method. It is illustrated by application to leak detection in a cascade of two heat exchangers.