The processing of zirconium ceramics requires special techniques and tools due to their inherent hardness and abrasion resistance. It is crucial to recognize the challenges of machining these ceramics, with the choice of machining method depending on the specific application requirements. In this article, the feasibility of machining non-conductive zirconium ceramics using electrical discharge machining (EDM) is investigated. The research presents an innovative approach using EDM with a hybrid auxiliary electrode consisting of a graphite coating and a copper strip. The copper foil contributes to the robustness and ensures the strength of the auxiliary electrode, while the graphite coating serves as an adhesive between the foil and the ceramic. The study investigates the individual effects of different input parameters such as discharge current and pulse duration on surface roughness, material removal rate and tool wear rate. The results of this investigation have a significant impact on the overall machining performance. In particular, the discharge current and pulse duration play an equally important role, as they have a direct effect on the total discharge energy. In addition, parameters such as duty cycle, open voltage and polarity are thoroughly analyzed. Furthermore, the initial investigation lays the foundation for establishing criteria in the main study, with the findings being seamlessly integrated into the machining process of zirconium ceramics. This comprehensive approach aims to improve the precision and efficiency of machining these challenging materials.