1. Introduetlon Recently Connes [5] made a significant progress in the classification of factors of type III. In particular, he proved that there exists a one-parameter family of non-isomorphic factors of type III without non-trivial central sequences, namely, the non-hyperfinite factors P~ (M2 in [10]) of Pukanszky. In another important paper [6], Connes proved that if a factor M has no non-trivial central sequence then the group Int(M) of all inner automorphisms of M is closed in the group Aut(M) of all automorphisms of M equipped with an appropriate topology (this result was obtained independently by Sakai [11] for the IIl-case ). In [3] Ching constructed a lit-factor M2.M 3, the free product of a 2 x 2 matrix algebra by a 3 x 3 matrix algebra, without non-trivial central sequence, and at present, we are not able to find an outer automorphism for it. For this factor M2.M 3 there remains the possibility that Int(M2.M3)=Aut(M2*M3). Takesaki [12] has shown, however, that a factor of type III always has an outer automorphism. Hence, it is of interest to see a type III version of the factor M2.M 3. The purpose of this paper is to construct such factors of type III, and classify them accordingly. We first generalize the crossed product ofa von Neumann algebra by a discrete group of automorphisms to the crossed product of avon Neumann algebra by a yon Neumann algebra with an ortho-unitary basis. We then construct a oneparameter family {Ma} of factors of type III using crossed products of hyperfinite factors of type III by M2*M 3. {M~} is shown to be a family of factors of type III without non-trivial central sequences. Finally, we prove that M~ is not isomorphic to M~, for 2.2'. The proof rely on a formula in Connes [51 but it is different from Conne's proof of the pairwise non-isomorphism of {Pa} as crossed products (Theorem 3.6.5 [5]) in the following respects: The "ratio set" r(G) of a transformation group introduced by Krieger [8] (based on the asymptotic ratio set of Araki and Woods) is not used here, and hence our approach is more direct in certain sense.