To improve the power of unit root test, the left adjustment method is applied to construct the Wald joint statistic and the distribution of statistic under the specific data generation process is also analyzed. Theoretical research shows that the statistic converges to the functional of Wiener process in distribution under large sample size, which is different from any of the existing statistic. Monte Carlo simulation shows two conclusions: first, the quantile of left adjusted Wald joint statistic decreases with the increase of sample size, and is less than that of corresponding unadjusted Wald joint statistic; second, the left adjusted Wald joint statistic not only has a satisfactory size level, but also owns the test power no less than that of the unadjusted Wald joint statistic. The results of this research can help improve the unit root joint test method and provide a new test method for empirical research, which enriches the theory of unit root test process.