  Let $S$ be a very general smooth hypersurface of degree $6$ in
$\mathbb{P}^3$. In this paper we will prove that the moduli space of
$\mu$-stable rank $2$ torsion free sheaves with respect to hyperplane section
having $c_1 = \mathcal{O}_S(1)$, with fixed $c_2 \ge 27$ is irreducible.
