  We prove the long time existence and uniqueness of solution to a parabolic
quaternionic Monge-Amp\`{e}re type equation on a compact hyperK\"{a}hler
manifold. We also show that after normalization, the solution converges
smoothly to the unique solution of the Monge-Amp\`{e}re equation for
$(n-1)$-quaternionic psh functions.
