Surface acoustic waves (SAW) propagating on magneto-strictive ferromagnets can induce mag-netization reversal: their weak damping and mature technology make them ideal for remote wave control of magnetic bits. Experimental demonstrations of this spectacular coupling have so far required the simultaneous application of a static magnetic field. We show here SAW-driven all-acoustical switching (AAS) over millimetric distances. It relies on the triggering of magnetization precession of a uniaxial in-plane magnetized film by acoustic ferromagnetic resonance at zero field. Moreover, the absence of biasing field enables toggling between the two equilibrium magnetic states for over twenty consecutive acoustic pulses. This proof-of-concept opens an alternative path to magnetic bit manipulation.