The problem of finding APN permutations of F_2ⁿ where n is even and n>6 has been called the Big APN Problem. Li, Li, Helleseth and Qu recently characterized APN functions defined on F_q² of the form f(x)=x^3q+a₁x^2q+1+a₂x^q+2+a₃x³, where q=2^m and m >= 4. We will call functions of this form Kim-type functions because they generalize the form of the Kim function that was used to construct an APN permutation of F_2⁶. We extend the result of Li, Li, Helleseth and Qu by proving that if a Kim-type function f is APN and m >= 4, then f is affine equivalent to one of two Gold functions G₁(x)=x³ or G₂(x)=x^2m-1+1. Combined with the recent result of Gologlu and Langevin who proved that, for even n, Gold APN functions are never CCZ equivalent to permutations, it follows that for m >= 4 Kim-type APN functions on F_2^2m are never CCZ equivalent to permutations.

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