Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. For A;B 2 B(H), define the bimultiplication operator M2;A;B on the class of Hilbert-Schmidt operators by M2;A;B(X) = AXB. In this paper, we show that if B, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) W0(M2;A;B); where co stands for the convex hull and W0(:) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2;A;B): [ABSTRACT FROM AUTHOR]