A total norm of τ-adic non-adjacent form occurring among all element of ℤ(τ): An alternative formula AIP Conference Proceedings 1795, 020002 (2017) Abstract. Bank industry plays a vital role in a country's economic development. In the banking industry, the nonperforming loans which are acknowledged as being undesirable outputs and usually ignored in most of the analysis should be taken into account since they are undesirable by-products of producing loans and may lead to the bank inefficiency. Modelling the efficiency measurement without undesirable outputs can provide misleading results and unfair assessment. The Directional Distance Function (DDF) approach which extended from the Data Envelopment Analysis (DEA) framework is one of the enhancement efficiency approaches to handle a situation when there is a joint production of the desirable and undesirable outputs. The comparison of both results between the domestic and foreign banks shows that the DEA technical efficiency score for domestic banks is marginally higher than the Malaysian foreign banks. However, when incorporating the undesirable output, the DDF technical efficiency for foreign banks is slightly higher than domestic banks.