We propose a Bayesian procedure to estimate heteroscedastic variances of the regression error term, when the form of heteroscedasticity is unknown. We use prior information that is elicited from the well-known Eicker--White Heteroscedasticity Consistent Variance-Covariance Matrix Estimator, and then use Markov Chain Monte Carlo algorithm to simulate posterior pdf's of the unknown heteroscedastic variances. In addition to numerical examples, we present an empirical investigation of the stock prices of Japanese pharmaceutical and biomedical companies.