The generation of an isolated relativistic attosecond electron bunch (RAEB) from the interaction of a laser with magnetized subcritical-density plasma is proposed. Particle-in-cell simulations show that a relativistic-intensity right-hand circularly polarized laser pulse can be much shortened and amplified if the magnetic field is along the laser propagation direction and the electron cyclotron frequency is appropriately larger than the laser frequency. In this case the plasma electrons are trapped in and propagate with the laser pulse like a solitary wave. The resulting charge separation field eventually causes the pulse to split into a forward propagating and a backward propagating pulse. Thus, the electrons in the latter are strongly pulled backwards by the ponderomotive force of the tail of the original laser pulse as well as the charge separation force, and eventually acquire the form of a RAEB of several attoseconds duration with a density of more than 5 times the critical density of the pristine plasma. The properties of the RAEB can be controlled by tailoring the initial laser and plasma parameters.