The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In this paper, we show that for\textit{ sufficiently large bandwidth} convergence is guaranteed in any dimension with \textit{any radially symmetric and strictly positive definite kernels}. Although the author acknowledges that our result is partially more restrictive than that of \cite{YT} due to the lower limit of the bandwidth, our kernel class is not covered by the kernel class in \cite{YT}, and the proof technique is different. Moreover, we show theoretically and experimentally that while for Gaussian kernel, accurate clustering at \textit{large bandwidths} is generally impossible, it may still be possible for other radially symmetric, strictly positive definite kernels.