When the eigenvalue decomposition(EVD) algorithm is used to estimate the basic function for transform domain communication systems(TDCS) under the asynchronous condition, the eigenvector got by the algorithm is fuzzy, thus degrading the system performance. A synchronous method of basis function is proposed to solve this problem. Based on a detailed study of the EVD algorithm, the relational expression of the data sampling delay and the eigenvalue of self-covariance matrix is deduced, and then a maximum likelihood(ML) estimation algorithm of the synchronization parameter is obtained. According to the norm-equivalence theorem, the frobenius norm is introduced in the problem of finding the largest eigenvalue in ML estimation algorithm, so the algorithm complexity is reduced. The simulation results show that the frobenius norm-based algorithm has the same performance as the largest eigenvalue-based algorithm but it only requires a less calculating time, and its estimation accuracy is in direct proportion to the signal-to-noise ratio(SNR). When the estimated basic function remains fuzzy under the asynchronous condition, the reception performance of the system can be improved by the use of basic function after synchronization.