A new almost perfect nonlinear function which is not quadratic

Following an example in [12],we show how to change one coordinate function of analmost perfect nonlinear(APN) function in order to obtain new examples. It turns out thatthis is a very powerful method to construct newAPN functions. In particular, we show that our approach canbe used to construct a ''non-quadratic'' APN function.This new exampleis in remarkable contrast to all recently constructed functions whichhave all been quadratic.An equivalent function has been found independentlyby Brinkmann and Leander [8]. However, theyclaimed that their function is CCZ equivalent to a quadratic one. In thispaper we give several reasonswhy this new function is not equivalent to a quadratic one.