A quadratic extension field (QEF) defined by F1 = Fp[α]/(α2+1) is typically used for a supersingular isogeny Diffie-Hellman (SIDH). However, there exist other attractive QEFs Fi that result in a competitive or rather efficient performing the SIDH comparing with that of F1. To exploit these QEFs without a time-consuming computation of the initial setting, the authors propose to convert existing parameter sets defined over F1 to Fi by using an isomorphic map F1 → Fi.