We can define a multiplication on the set "S" using the Steiner triple system by setting "aa" = "a" for all "a" in "S", and "ab" = "c" if {"a","b","c"} is a triple. This makes "S" an idempotent, commutative quasigroup. It has the additional property that "ab" = "c" implies "bc" = "a" and "ca" = "b". Conversely, any (finite) quasigroup with these properties arises from a Steiner triple system. Commutative idempotent quasigroups satisfying this additional property are called "Steiner quasigroups".