This study revisits the privatization neutrality theorem that claims that social welfare is exactly the same before and after privatization when the government gives the optimal subsidy to both public and private firms in a mixed oligopoly. Unlike the existing literature that has assumed that a uniform subsidy is given to public and private firms, we demonstrate that if the discriminatory subsidy rates are adopted even when there is firm asymmetry between public and private firms, the privatization neutrality theorem continues to hold. First, we show that even if the cost of the public firm differs from those of private firms, the privatization neutrality theorem holds by appropriately subsidizing both public and private firms at the different levels. Second, even if the public firm acts as a Stackelberg leader before and after privatization, the government can attain privatization neutrality by adopting the discriminatory subsidy and, as a result, can achieve social welfare maximization. Our result suggests that even when there exists firm asymmetry between public and private firms, it is not important for privatization authorities to determine whether to privatize the public firm.