In this paper we propose a new ILP method Bottom Reduction. It is an extension of Bottom Generalization for treating multiple examples. Using Bottom Reduction we can find all hypotheses which subsume all of given examples relative to a background theory in Plotkin's sense. We do not assume any restriction on the head predicates of the examples. Applying Bottom Reduction to examples which have a predicate different from those of other examples, we can reduce the search space of hypotheses. We have already implemented a simple learning system named BORDA based on Bottom Reduction on a Prolog system, and we present, in this paper, some techniques in its implementation.