In Brock's (1964) analysis concerning the thermophoretic force on a small particle suspended in a rarefied plasma with a temperature gradient, the effect of the presence of an external magnetic field on the ion and electron components of the thermophoretic force was demonstrated. The particle suspended in the plasma was assumed to be electrically neutral, which is obviously not realistic. Consequently, Brock obtained similar expressions for the thermophoretic force components due to, respectively, atoms, ions and electrons for the case without the external magnetic field. The present paper improves Brock's analysis by taking the charging of the suspended particle into account and obtains somewhat different expressions from his results for the thermophoretic force components due to ions and electrons.