  The problem of decomposition of bilinear forms which satisfy a certain
condition has been studied by many authors by example in \cite{H08}: Let $H$
and $K$ be Hilbert spaces and let $A,C \in B(H),B,D\in B(K)$. Assume that
$u:H\times Karrow \C$ a bilinear form satisfies \[ |u(x,y)|\leq\|Ax\|\
\|By\|+\|Cx\|\|Dy\| \] for all $ x\in H$ and $y\in K$. Then u can be decomposed
as a sum of two bilinear forms \[ u=u_1+u_2 \] where \[ |u_1(x,y)|\leq \|Ax\|\
\|By\|, |u_2(x,y)|\leq \|Cx\|\|Dy\|, \forall x\in H,y\in K. \] U.Haagerup
conjectured that an analogous decomposition as a sum of bounded bilinear forms
is not always possible for more than two terms. The aim of current paper is to
investigate this problem. In the finite dimensional case, we give a necessary
and sufficient criterion for such a decomposition. Finally, we use this
criterion to give an example of a sesquilinear form $u$, even on a
two-dimensional Hilbert space, which is majorized by the sum of the moduli of
three bounded forms $b_1,b_2$ and $b_3$, but can not be decomposed as a sum of
three sesquilinear forms $u_i$ where each $u_i$ is majorized by the
corresponding $|b_i
