Recently, there has been an increased usage of NiTi shape memory alloys in biomedical and other industrial applications due to their special properties such as shape memory effect, superelasticity, and high strength to density characteristics etc. But, due to their poor machinability, the advanced processes are being explored for their successful machining i.e. better machinability. This paper reports a part of research conducted on the machining of Ni_55.8Ti by wire electric discharge cutting (WEDC). In the Taguchi L₁₆ orthogonal array based experimental study, four important WEDC parameters namely gap voltage, pulse on-time, off-time and wire feed rate have been varied and their effects are analyzed on micro-hardness (which is an important machinability indicator) of the shape memory alloy specimen. ANOVA and Taguchi based optimization of WEDC parameters has also been done to secure the best value of the micro-hardness.