Based on the completeness of the real-valued discrete Gabor transform, a new biorthogonal relationship between analysis window and synthesis window is derived and a fast algorithm for computing the analysis window is presented for any given synthesis window. The new biorthogonal relationship can be expressed as a linear equation set, which can be separated into a certain number of independent sub-equation sets, where each of them can be fast and independently solved by using convolution operations and FFT to obtain the analysis window for any given synthesis window. Computational complexity analysis and comparison indicate that the proposed algorithm can save a considerable amount of computation and is more efficient than the existing algorithms.