Electrical discharge machining (EDM) is one of the most extensively used non-conventional material removal processes. The Taguchi method has been utilized to determine the optimal EDM conditions in several industrial fields. The method, however, was designed to optimize only a single performance characteristic. To remove that limitation, the Grey relational analysis theory has been used to resolve the complicated interrelationships among the multiple performance characteristics. In the present study, we attempted to find the optimal machining conditions under which the micro-hole can be formed to a minimum diameter and a maximum aspect ratio. The Taguchi method was used to determine the relations between machining parameters and process characteristics. It was found that electrode wear and the entrance and exit clearances had 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 parameters, among which the input voltage and the capacitance were found to be the most significant. The obtained optimal machining conditions were an input voltage of 60V, a capacitance of 680pF, a resistance of 500$Omega$, the feed rate of $1.5{mu}m$/s and a spindle speed of 1500rpm. Under these conditions, a micro-hole of $40{mu}m$ average diameter and 10 aspect ratio could be machined.