We propose a Bayesian procedure to estimate heteroskedastic variance vector of the regression error term, when the form of heteroskedasticity is unknown. We use a Dirichlet prior on . Information from the well known Eicker-White HCE (Heteroskedasticity Consistent Variance-Covariance Matrix Estimator) is used to simulate in Markov Chain Monte Carlo. Bayesian interests on may go back to Geweke (1993), where he was mainly interested in estimating regression slope coefficients. He started out with a heteroskedastic NLR (normal linear regression) model but reduced it to a homoskedastic fat tailed Student-t error term model. We shall find out the relationship between our procedure and that of Geweke's.