Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this paper, we present a new construction of differentially 4-uniformity permutations over even characteristic finite fields and obtain many new CCZ-inequivalent functions. All the functions are switching neighbors in the narrow sense of the multiplicative inverse function and have the optimal algebraic degree and high nonlinearity.