The Ising spin system is discussed in which the interaction of spins with heat bath causes the spontaneous flip of spins. It is assumed that the system is in thermal equilibrium up to some instant under a uniform and sufficiently small magnetic field and the magnetic field is switched off at that instant. The initial decay of magnetization in such a situation is studied. In the neighborhood of transition point, it is proved that a relaxation time associated with the initial decay is proportional to the susceptibility, and an exact proportionality constant is calculated for the two-dimensional square lattice with nearest-neighbor interaction.