  The characterization of bipartite distance-regularized graphs, where some
vertices have eccentricity less than four, in terms of the incidence structures
of which they are incidence graphs, is known. In this paper we prove that there
is a one-to-one correspondence between the incidence graphs of quasi-symmetric
SPBIBDs with parameters $(v,b,r,k, \lambda_1,0)$ of type $(k-1,t)$ with
intersection numbers $x=0$ and $y>0$, where $0< y\leq t<k$ , and bipartite
distance-regularized graphs with $D=D'=4$.
