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We demonstrate that the magnetization of a ferromagnet in contact with an antiferromagnetic multiferroic () can be speedily reversed by electric-field pulsing, and the sign of the magnetic exchange bias can switch and recover isothermally. As is not ferroelastic, our data conclusively show that this switching is not mediated by strain effects but is a unique electric-field driven decoupling of the ferroelectric and antiferromagnetic domain walls. Their distinct dynamics are essential for the observed magnetic switching.