Let $M$ be an irreducible hyperkähler manifold and $\mathcal{L}$ a non-trivial nef bundle on $M$, with $q_{M}(c_{1}(\mathcal{L}))=0$. Then $\mathcal{L}$ induces a holomorphic map $f^{\prime}:M\rightarrow N^{\prime}$ to a projective variety $N^{\prime}$ with $\mathcal{L}^{m}\cong f^{\prime*}(\mathcal{O}(1))$ for some $m>0$.