The combination of higher-order subtyping with intersection types yields a typed model of object-oriented programming with multiple inheritance [11]. The target calculus, F ! , a natural generalization of Girard's system F ! with intersection types and bounded polymorphism, is of independent interest, and is our subject of study. Our main contribution is the proof that subtyping in F ! is decidable. This yields as a corollary the decidability of subtyping in F ! , its intersection free fragment, because the F ! subtyping system is a conservative extension of that of F ! . The calculus presented in [8] has no reductions on types. In the F ! subtyping system the presence of fi-conversion -- an extension of fi-conversion with distributivity laws -- drastically increases the complexity of proving the decidability of the subtyping relation. Our proof consists of, firstly, defining an algorithmic presentation of the subtyping system of F ! , secondly, proving that th...