The convolution operator \(K\) defined by \(Kf= k*f\) on a compact connected semisimple Lie group \(G\) is considered, where \(k\) belongs to some class \(D^h\) of distributions. The operator \(K\) is proved to be of type \(\left({1\over 2},{1\over 2}\right)\). The proof is performed first for \(G=\text{SU}(2)\) and then extended to the general case.