Recently, the special kind of near-regular texture has drawn significant attention from researchers in the field of texture synthesis. Near-regular textures contain global regular structures that pose significant problems to the popular sample-based approaches, and irregular stochastic structures that can not be reproduced by simple tiling. Existing work tries to overcome this problem by user assisted modeling of the regular structures and then relies on regular tiling. In this paper we use the concept of fractional Fourier analysis to perform a fully automatic separation of the global regular structure from the irregular structure. The actual synthesis is performed by generating a fractional Fourier texture mask from the extracted global regular structure which is used to guide the synthesis of irregular texture details. Our new method allows for automatic and efficient synthesis of a wide range of near-regular textures preserving their regular structures and faithfully reproducing their stochastic elements.