We propose a Bayesian procedure to estimate possibly heteroscedastic variances of the regression error term, without assuming any structure on them. In our previous paper, i.e., Hi-Stat D.P. #185, we said that our method is a "Conditional Bayesian" in the sense that our Bayesian framework depended on the Eicker-White Heteroskedasticity Consistent Covariance Matrix Estimator, a well known sampling theory result. In the present paper, we develop a fully Bayesian framework to estimate unknown heteroskedastic variances. In addition to the numerical examples, we may present an empirical investigation on the stock prices of Japanese pharmaceutical and biomedical companies.