A new Brownian dynamics simulation technique is presented for the calculation of the effective rate constant for diffusion controlled reactions with a finite intrinsic reactivity. The technique is based on the calculation of the recollision probability of a molecule with a reactive site using a large number of Brownian trajectories, when the probability of reaction upon collision with the reactive site (phi(f)) is less than unity. The technique is a modification of the earlier work of Northrup et al. [J. Chem. Phys. 80, 1517 (1984)], and is applied to the case of a uniformly reactive target sphere and a target sphere with axially symmetric reactive patches. A theoretical analysis is presented to relate phi(f) to the intrinsic surface reaction rate constant (k’). Computational results for the uniformly reactive sphere are in excellent agreement with theory, and those for the sphere with patches are in very good agreement with the results obtained using a different computational technique [Allison ct al., J. Phys. Chem. 94, 7133 (1990)]. The proposed method requires the computation of the recollision probability to a high accuracy; however, this does not result in computational times greater than those of Allison er al. [J. Phys. Chem. 94, 7133 (1990)]. The new method has the advantage that the results of the Brownian dynamics simulation are independent of k’ and can subsequently be used to calculate the effective rate constant for any given value of k’.