This note deals with the estimations of the variance of a normal distribution $N( heta,c heta^2)$ where c, the square of coefficient of variation is assumed to be known. This amounts to the estimation of $ heta^2$. The minimum variance estimator among all unbiased estimators linear in $ar{x}^2$ and $s^2$ where $ar{x}$ and $s^2$ are the sample mean and variance, respectively, and the minimum risk estimator in the class of all estimators linear in $ar{x}^2$ and $s^2$ are obtained. It is shown that the suggested estimators are BAN.