A previous method of the author to calculate the second virial coefficients of pure compounds is re-considered in order to improve the reliability of the predictions and to reduce the number of the empirical constants required by the method. The method hinges only on the critical constants and the normal boiling temperature for any kind of compound, including the strongly associated ones. A comparison is made with the Pitzer-Tsonopoulos equation on the basis of the prediction of the B data of nearly 70 well studied compounds. The proposed method can be used also to evaluate the thermodynamic consistency of the B experimental data.