In this paper, we propose a new class of MIN (Multistage Interconnection Network) called SCMIN(ShortCut MIN) which can form a cheap and efficient packet switching interconnection network. SCMIN satisfies full access capability(FAC) and has multiple redundant paths between processor-memory pairs even though SCMIN is constructed with 2.5N-4 SEs which is far fewer SEs than that of MINs. SCMIN can be constructed suitable for localized communication by providing the shortcut path and multiple paths inside the processor-memory cluster which has frequent data communications. Therefore, SCMIN can be used as an attractive interconnection network for parallel applications with a localized communication pattern in shared-memory multiprocessor systems.