Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spatial Covariance Analysis (FCA), which is a robust audio source separation method proposed by Duong et al. ["Under-determined reverberant audio source separation using a full-rank spatial covariance model," IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830-1840, Sept. 2010]. In the conventional FCA, matrix inversion and matrix multiplication are required at each time-frequency point in each iteration of an iterative parameter estimation algorithm. This causes a heavy computational load, thereby rendering the FCA infeasible in many applications. To overcome this drawback, we take a joint diagonalization approach, whereby matrix inversion and matrix multiplication are reduced to mere inversion and multiplication of diagonal entries. This makes the FastFCA-AS significantly faster than the FCA and even applicable to observed data of long duration or a situation with restricted computational resources. Although we have already proposed another acceleration of the FCA for two sources, the proposed FastFCA-AS is applicable to an arbitrary number of sources. In an experiment with three sources and three microphones, the FastFCA-AS was over 420 times faster than the FCA with a slightly better source separation performance.