It is known that although the Baer Criterion for injectivity holds for modules over rings with unit, it is not true for acts over an arbitrary monoid. Recently, the present author, together with M. Ebrahimi and M. Mahmoudi, published a paper (Comm. Algebra 35 (2007), 3912- 3918) giving for the acts over some classes of semigroups, the Baer Criterion is true. In this paper we find another classe of monoids such that for acts over them the Baer Criterion holds.