  In this paper we define the concept of orthogonality between two factors
"through another factor". Exploiting this property we have been able to obtain
orthogonal main effect plans (OMEP) on non-orthogonal blocks requiring
considerably smaller number of blocks than the existing methods. As particular
cases, we have been able to accomodate four six-level factors on 8 blocks of
size 4 each using the first method and on 24 runs using the second.
