The index of a signed graph \Sigma = (G; \sigma) is just the largest eigenvalue
of its adjacency matrix. For any n > 4 we identify the signed graphs achieving the
minimum index in the class of signed bicyclic graphs with n vertices. Apart from the n = 4 case, such graphs are obtained by considering a starlike tree with four branches of suitable length (i.e. four distinct paths joined at their end vertex u) with two additional negative independent edges pairwise joining the four vertices adjacent to u. As a by-product, all signed bicyclic graphs containing a theta-graph and whose index is less than 2 are detected
