Abstract: The effectiveness, error formula, algorithm flow, and weak classifiers training of Real AdaBoost algorithm are analyzed and proved by a new technique. Real AdaBoost algorithm is improved by weighted combination of weak classifiers and the approximately best combination coefficients are obtained. It is proved that the function of sample weight adjusting method and weak classifiers training method is to guarantee the independence of weak classifiers. Multi-class Real AdaBoost algorithm is proposed based on Bayes statistics deduction. The formula of algorithm and the estimation of classification error are discussed. The training method of weak classifiers is simplified. The estimation of classification error of Gentle AdaBoost is obtained. The effectiveness of the proposed algorithms is verified by the experiment on UCI dataset.