Oberwolfach rectangular table negotiation problem

We completely solve certain case of a ''two delegation negotiation'' version of the Oberwolfach problem, which can be stated as follows. Let H(k,3) be a bipartite graph with bipartition X={x"1,x"2,...,x"k},Y={y"1,y"2,...,y"k} and edges x"1y"1,x"1y"2,x"ky"k"-"1,x"ky"k, and x"iy"i"-"1,x"iy"i,x"iy"i"+"1 for i=2,3,...,k-1. We completely characterize all complete bipartite graphs K"n","n that can be factorized into factors isomorphic to G=mH(k,3), where k is odd and mH(k,3) is the graph consisting of m disjoint copies of H(k,3).