  Consider a qubit-qutrit ($2 \times 3$) composite state space. Let
$C(\{1}{2}I_2, \{1}{3}I_3)$ be a convex set of all possible states of composite
system whose marginals are given by $\{1}{2}I_2$ and $\{1}{3}I_3$ in two and
three dimensional spaces respectively. We prove that there exists no pure state
in $C(\{1}{2}I_2, \{1}{3}I_3)$. Further we generalize this result to an
arbitrary $m \times n$ bipartite systems. We prove that for $m < n$, no pure
state exists in the convex set $C(\rho_A,\rho_B)$, for an arbitrary $\rho_A$
and rank of $\rho_B >m$.
