  In 1994 Drew, Johnson and Loewy conjectured that for $n \ge 4$, the cp-rank
of any $n\times n$ completely positive matrices is at most
$\lfloor{n^2}/{4}\rfloor$. Recently this conjecture has been proved for $n=5$
and disproved for $n\ge 7$, leaving the case $n=6$ open. We make a step toward
proving the conjecture for $n=6$. We show that if $A$ is a $6\times 6$
completely positive matrix that is orthogonal to an exceptional extremal
copositive matrix, then the cp-rank of $A$ is at most $9$.
