The bytecode verifier of the Java Virtual Machine, which statically checks the type safety of Java bytecode, is the basis of the security model of Java and guarantees the safety of mobile code sent from an untrusted remote host. However, the type system for Java bytecode has some technical problems, one of which is in the handling of sub-routines. Based on the work of Stata and Abadi and that of Qian, this paper presents yet another type system for Java Virtual Machine sub-routines. Our type system includes types of the form last(x). A value whose type is last(x) is the same as that of the x-th variable of the caller of the subroutine. In addition, we represent the type of a return address by the form return(n), which means returning to the n-th outer caller. By virtue of these types, we can analyze instructions purely in terms of type, and as a result the correctness proof of bytecode verification becomes extremely simple. Moreover, for some programs, our method is more powerful than existing ones. In particular, our method has no restrictions on the number of entries and exits of a subroutine.