In this paper we will present a syntactic decision procedure for the disjunction-free fragment of $H$. With the help of a result of A. Diego [3] we will show that any decision procedure for the disjunction-free fragment of $H$, and hence also ours, can serve for all finitely axiomatizable disjunction-free intermediate logics. These logics were proved decidable in [6] also with the help of Diego's result.