The idea of a discrete
w
(
x
,
y
)
=
v
(
x
,
y
)
w(x,y) = v(x,y)
quasigroup is given along with a generalization of A. Sade’s singular direct product. These notions are then used to construct certain types of quasigroups. In particular an algebraic generalization of E. H. Moore’s construction of Steiner triple systems is obtained.