In this note, we give a certain class of cuspidal prehomogeneous vector spaces and determine explicitly two basic relative invariants of a cuspidal prehomogeneous vector space (GL(4) × GL(3)×SL(2),Λ?1 ?1?1+Λ1 ?Λ?1 ?Λ?1 ,M(1, 4)?M(4, 3)?M(4, 3)) which is a special case of the class. We consider everything over the complex number field C.Representation Theory of Algebraic Groups and Related Topics : Proceedings of the workshop on Representation Theory, September 15,16, 2012 JOSAI UNIVERSITY / edited by Masatoshi IIDA, Takeyoshi KOGISO, Haruko NISHI, Kiyoko NISHIZAWA. The first author is partially supported by the grant in aid of scientific research of JSPS No.24540049.