This paper revisits this problem of finding the best rank-1 approximation to a symmetric tensor and makes three contributions. First, in contrast to the many long and lingering arguments in the literature, it offers a straightforward justification that generically the best rank-1 approximation to a symmetric tensor is symmetric. Second, in contrast to the typical workhorse in the practice for the low-rank tensor approximation, namely, the alternating least squares (ALS) technique which improves one factor a time, this paper proposes three alternative algorithms, based on the singular value decomposition (SVD) that modifies two factors a time. One step of SVD-based iteration is superior to two steps of ALS iterations. Third, it is proved that not only the generalized Rayleigh quotients generated from the three SVD-based algorithms enjoy monotone convergence, but also that the iterates themselves converge.