A polynomial ???? over a finite field ???????? is called a permutation polynomial if its associate function ????:????????→???????? is a bijective mapping. If ????(????+????)−????(????) is a permutation polynomial of ???????? for every ????∈????????∗ , then the polynomial ????(????) is said to be perfect nonlinear or planar. Perfect nonlinear functions are closely related to permutation polynomials. In this article we propose a class of perfect nonlinear function over ????????4. We also characterize a family of DO-polynomials of the form Σ????????????????????????+????????????−1????,????=0 to be perfect nonlinear function over ????????????.