It is shown that a quasi-residual 2-(v, k, λ) design is the residuum of a symmetric design provided that k > cλ 4 for a constant number c. This result improves earlier results of Bose et al. (1976) and Neumaier (1982), who proved the result for k > 1λ 5 + 0(λ 4 ). This embedding theorem will be a consequence of more general characterization theorems for certain strongly regular multigraphs (see Theorem 2 and its corollary in the introduction).