  Keeping in view the suggestion of Barr and Marciano [7] that the cut of
procedure involves a good deal of uncertainity in the prediction of E.D.M. of W
- boson, we have re-examined the earlier calculation by Marciano and Queijeiro
[2] by replacing the Cut-off regularization process by BPHZ regularization[8].
This works in a clean and unambiguous manner without involving any
approximation. We also examine apparently inapplicable approximations like
using m(f) = m(f')in [2]. The bounds on lambda(w) and d(w) are significantly
changed in all cases as compared with those reported in [2]. The necessary
caution that is to be excercised while using approximations is explicitly
pointed out. PACS number (s): 13.40. Em
