Response adaptive designs are developed for ethical considerations, which sequentially modify the treatment allocations based on the accumulating information in the trial so more patients receive the potentially better treatment. Yi and Wang (2009) proposed a variance-penalized criterion to evaluate the performance of a response adaptive design based on the expected number of patients assigned to the better treatment and the power of statistical test. We use the variance-penalized criterion to examine different response adaptive randomization procedures for normally distributed responses. We propose a new target allocation proportion which increases the chance that more patients receive the better treatment. Simulation results indicate that our proposed design has the advantage of assigning more patients to the potentially better treatment with minimum loss in statistical power, and our design performs better than the designs in the literature based on the variance-penalized criterion.