We describe a method for estimating rate constants of a two-state Markov system from data obtained by a single-molecule (SM) type of experiment corrupted by white noise. The method is effective even when the characteristic (or resolution) time of the measurement is much longer than a characteristic time of the two-state system, and the data are uncorrelated. We apply our suggested method to data from an SM:experiment on the transport of sugar molecules through cell membrane channels. The method is quite accurate in analyzing this set of data. We also demonstrate that in some cases the method can be used to check whether the system is Markovian or not.