  Let $X$ be a smooth projective curve of genus $g$ and $L$ be a degree $l$
line bundle on $X$ with $l\geq 2g-1$. Denote the stack of rank two Higgs
bundles on $X$ with value in $L$ by $\mathcal{H}iggs$ and the semistable part
by $\mathcal{H}iggs_{ss}$. Let $H$ be the Hitchin base. In this paper we will
construct the Poincare sheaf $\mathcal{P}$ on
$\mathcal{H}iggs\times_{H}\mathcal{H}iggs_{ss}$ which is a maximal
Cohen-Macaulay sheaf and flat over $\mathcal{H}iggs_{ss}$. In particular this
includes the locus of nonreduced spectral curves.
