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This paper is a continuation of the previous paper [2] by the first named author. The deformation of partially complex structures on a compact strongly pseudo-convex manifold was investigated first by M. Kuranishi [4] in order to give a new insight into the problem of deformations of isolated singularities, and he constructed a family of partially complex structures on a compact strongly pseudo-convex real hypersurface of a complex analytic space with an isolated singularity parametrized by a finite number of parameters and inducing the versal family of deformations of the isolated singularity in some sense. If (K, x) is an analytic subset of a domain in a complex euclidean space with an isolated singular point x, we obtain a real submanifold M by cutting the analytic set by a sphere of sufficiently small radius centered at x, and V defines a subbundle °T" of CTM, which is called the partially complex structure on M induced from V, consisting of all tangent vectors of type (0, 1) in C7YJM. Kuranishi represented an almost partially complex structure on M of finite distance from °T" by an element of F(M, T'®(°T")*) and constructed the above-mentioned family of integrable almost partially complex structures making use of the harmonic theory for Ob. He tided over the difficulties arising from the non-ellipticity of Sb by making use of Nash-Moser's inverse mapping theorem, thereby the family has only a differentiable structure of class C°°. Then the problem as to when the family may have a complex analytic structure was left open. The first named author answered this problem affirmatively in

Complex analytic construction of the Kuranishi family on a normal strongly pseudoconvex manifold. II