Abstract: Uniform acceptance force biased Monte Carlo (UFMC) simulations have previously been shown to be a powerful tool to simulate atomic scale processes, enabling one to follow the dynamical path during the simulation. In this contribution, we present a simple proof to demonstrate that this uniform acceptance still complies with the condition of detailed balance, on the condition that the characteristic parameter lambda = 1/2 and that the maximum allowed step size is chosen to be sufficiently small. Furthermore, the relation to Metropolis Monte Carlo (MMC) is also established, and it is shown that UFMC reduces to MMC by choosing the characteristic parameter lambda = 0 [Rao, M. et al. Mol. Phys. 1979, 37, 1773]. Finally, a simple example compares the UFMC and MMC methods.