Recently, Lam [1] developed a two-step method to find the most efficient (the best) unit in Data Envelopment Analysis (DEA). The first step finds an appropriate value for the epsilon to use in the second step to find the best unit. Salahi and Toloo [2] showed that the approach of Lam [1] may fail to determine the best unit. To fill this gap, they proposed a new model to find a suitable value for the epsilon in the first step. The current paper shows that in some cases, we may have several most efficient DMUs such that we could not easily discriminate among them to determine one of them as the best DMU. Also, we show that the second step in the proposed approach by Lam and Salahi and Toloo, is redundant. We propose an improved approach that can find the best DMU by solving only one model. As a result, the calculation burden of the new approach is significantly less than the two mentioned approaches. A real numerical example is used to compare the results and show the usefulness of the new approach.