We find that the star formation is accelerated by the supersonic turbulence in the magnetically dominated (subcritical) clouds. We employ a fully three-dimensional simulation to study the role of magnetic fields and ion-neutral friction in regulating gravitationally driven fragmentation of molecular clouds. The time-scale of collapsing core formation in subcritical clouds is a few ×107 years when starting with small subsonic perturbations. However, it is shortened to approximately several ×106 years by the supersonic flows in the clouds. We confirm that higher-spacial resolution simulations also show the same result.