**Subalgebras of finite minimal majority algebras revisited**

If A is a minimal algebra then the set S_2(A) of all subalgebras of
A\times A has a natural structure of ordered involutive monoid. In recent
years I have tried to find an abstract characterization of
S_2(A) provided A is a finite majority algebra. For some time I have been
quite sure that this characterization consists of two conditions:
distributivity and completeness. Recently it turned out that one more
condition has to be added.