AbstractA strongly regular decomposition of a strongly regular graph is a partition of the vertex set into two parts on which the induced subgraphs are strongly regular, or cliques or cocliques. Strongly regular designs (srd's) as defined by D. G. Higman are coherent configurations of rank 10 with two fibers in which the homogeneous configuration on each fiber is a strongly regular graph. Haemers and Higman proved the equivalence between strongly regular decompositions, excluding special cases, and srd's with certain parameter conditions. Here we obtain this result by examining the srd's that admit a fusion to a strongly regular graph on the full vertex set. We derive equivalent conditions to Theorem 2.8 of Haemers and Higman by elementary methods. Incorporating recent works of Hanaki and Klin and Reichard, a table of feasible parameter sets for this class of srd's is presented along with a discussion of known constructions. In two cases, nonexistence is observed due to nonexistence of the strongly regular graph obtained through fusion. One of these is also ruled out by Hobart's generalized Krein conditions, applied to srd's. As strongly regular decompositions of the complete graph have sparked interest with recent papers we observe that in our situation this occurs only when the constituent graphs are also complete and the design is trivial.