Abstract: The short time fractional Fourier transform (STFRFT) is a useful tool for the research on analysis and recognition of multi-component non-linear frequency modulation (NLFM) signals, which have been presented on a lot of communication systems and radar systems. This paper investigates the non-circularity of STFRFT coefficients, and proposes a modified STFRFT such that all coefficients coming from white Gaussian noise are circular. In order to use the spectral kurtosis (SK) as a Gaussian test to check if signal points are present in a set of STFRFT points, we study the SK of different points in the time-frequency transform figure, and propose the definition of the local SK. Finally, a time-frequency segmentation algorithm based on the region growing by the local SK is proposed to separate the multi-component NLFM signals. The effectiveness and robustness of this algorithm are evaluated via simulations.