The authors determine the graph with maximal spectral radius among connected bicyclic graphs of order \(n\), possessing \(k\) pendent vertices. This is the graph having two triangles with a common vertex at which \(k\) paths of almost equal length are attached. In fact, this paper finishes previous research on the topic since in the paper by the third author [Linear Algebra Appl. 408, 75--85 (2005; Zbl 1073.05550)] the problem of finding extremal graphs was reduced to just two candidates.