In our previous paper, we calculated out and determined the atomic unit of time (tau) to be 2.41888432658653284(45)×10-17 s. In this paper, using the BIPM recommended 171Yb atomic transition frequency which is 518295836590863.63(10) Hz and its reciprocal in atomic units calculated from our corresponding formula, we once more calculate out and determine the atomic unit of time to be 2.41888432658653280(46)×10-17 s. With this very slightly revised atomic unit of time and the reciprocal of 40Ca atomic transition frequency in atomic units calculated from our corresponding formula, we calculate out the 40Ca atomic transition frequency to be 455986240494140.30(9) Hz, which is about 94 times more precise than the BIPM recommended value, i.e., 455986240494140(8) Hz. Employing the same method, we also calculate out two 171Yb+ ionic transition frequencies which are consistent with the BIPM recommended values.