In this paper, we provide a direct proof of the fact that the symmetric embedding of B(H) into any of its bimodules induced by Markov maps is compact and establishes that this property characterizes type I factors. This is an extension of a result of D. Buchholz, C. D'Antoni, and R. Longo [J. Funct. Anal. 88(2), 233-250 (1990)]. © 2021 Author(s).