A canonical double cover of a graph is the direct product of and the complete graph on two vertices. In order to answer the question when a canonical double cover of a given graph is a Cayley graph, in 1992 Maru?i? et al. introduced the concept of generalized Cayley graphs. In this paper this concept is generalized to a wider class of graphs, the so-called extended generalized Cayley graphs. It is proved that the canonical double cover of a connected non-bipartite graph is a Cayley graph if and only if is an extended generalized Cayley graph. This corrects an incorrectly stated claim in [Discrete Math. 102 (1992), 279–285].