Micro electrical discharge machining (${mu}EDM$) has been used for non-conventional material removal. One drawback of ${mu}EDM$ is low productivity. In this study, we tried to find the optimal machining conditions to manufacture the micro hole with an optimal machining time without loss of accuracy. Taguchi method was used to figure out the relation between machining parameters and characteristics of the process. It was found that the electrode wear, the entrance and exit clearance gave a significant effect on the diameter of the micro hole when the diameter of the electrode was identical. Grey relational analysis was used to determine the optimal machining condition for minimum machining time without loss of accuracy. The obtained optimal machining condition was the input voltage of 80V, the capacitance of 680pF, the resistance of $500{Omega}$, the feed rate of $1.5{mu}m$/s and the spindle speed of 2900rpm. The machining time was reduced to 48% without loss of accuracy under the optimal machining condition.