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This paper develops a range directional distance data envelopment analysis (DEA) model to simultaneously deal with the problems of negative data and undesirable outputs in the study of performance measurement with two-stage DEA. We report on the development of this model to handle both positive and negative data in a DEA framework and accommodate the problem of undesirable intermediate outputs in the first stage of operational processes. Unlike previous two-stage DEA models we allow for a nonuniform abatement factor imposing on stage 1' production technology. Such a model is then applied to evaluate Taiwanese bank efficiencies both at the operational stage and profitability stage in banking activities based on a data set consisting of 35 domestic banks in Taiwan in the period 2007. The results indicate that, by the range directional two-stage data envelopment analysis model, the operational efficiency was smaller than the profitability efficiency. Many banks generated too many performing loans in which independent banks should reduce more performing loans than financial holding company subsidiary banks. Both the ratio of investments to loans and the ratio of nonperforming loans to performing loans did not have significant contributions to the efficiency. This paper is able to provide information for bank operators and researchers on the managerial and strategic implications of how negative data and undesirable outputs affect efficiency and how to measure efficiency appropriately. [ABSTRACT FROM AUTHOR]