We develop a conditional sampling scheme for pricing knock-out barrier options under the linear transformation algorithm from Imai and Tan [J. Comput. Finance, 10 (2006), pp. 129--155]. We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum [Oper. Res., 49 (2001), pp. 923--937] and show that a substantial variance reduction is achieved. We extend the method to allow pricing knock-in barrier options and introduce a root-finding method to obtain a further variance reduction. The effectiveness of the new method is supported by numerical results.