The Fourier series(FS) with fractional frequency intervals(FFFS) for the decomposition of signals is proposed.FFFS consists of sine and cosine functions,which is similar to FS,but the frequency intervals of the trigonometric functions don't have to be integers.Therefore,the decomposition of signal by FFFS is more flexible and precise.Two algorithms to choose the best frequency intervals are put forward.Compared with FS,FFFS has better performance in frequency-width,approach-items,approach-precise and Gibbs phenomenon.