Abstract. A binary relation $\rho $ on a set $U$ is strongly rigid if every universal algebra on $U$ such that $\rho $ is a subuniverse of its square is trivial. Rosenberg (1973) found a strongly rigid relation on every universe $U$ of at least 3 elements. We exhibit a new strongly rigid relation for every finite $U$ with $|U|\ge3$. We also show that, for $|U|=3$, there are only 2 strongly rigid binary relations up to isomorphism.

AMS Subject Classification (1991): 08A40

Received July 25, 1994, and in revised form November 8, 1994. (Registered under 5670/2009.)