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In this paper, we extend the result of Kitaev and Korotkin to the case wherea monodromy-preserving deformation has an irregular singularity. For themonodromy-preserving deformation, we obtain the $\tau$-function whosedeformation parameters are the positions of regular singularities and theparameter $t$ of an irregular singularity. Furthermore, the $\tau$-function isexpressed by the hyperelliptic $\Theta$ function moving the argument $\z$ andthe period $\B,$ where $t$ and the positions of regular singularities move $z$and $\B,$ respectively.

Isomonodromic deformatiion with an irregular singularity and hyperelliptic curve