We compute the Casimir pressure between an unusual pair of parallel plates, namely, a perfectly conducting plate (<FONT FACE="Symbol">e®¥)</font> and an infinitely permeable one (<FONT FACE="Symbol">m®¥</font>) with the generalized <FONT FACE="Symbol">z</font>-function method. The result for this problem, which has been rarely discussed in the literature, is a repulsive Casimir force. The <FONT FACE="Symbol">z</font>-function method provides a very compact and economic way of obtaining the final result.