Two aspects of problems such as weight over-bounding and reliability-dependence cannot be well solved in the evidential reasoning (ER) approach with both weight and reliability. In order to solve the above problems, the characteristics of weight and reliability are investigated and summarized, i.e., the reliability of evidence is objective and absolute to reflect information quality, while the weight of evidence is subjective and relative to reflect information importance. Then a new discounting method is defined to generate probability masses for the evidence by assigning residual support of weight to empty set and that of reliability to power set. A new ER rule is established for recursively combining the evidence with both reliability and weight by the orthogonal sum operation and a series of theorems and corollaries are introduced and proved. Finally numerical comparison and illustrative example are provided to demonstrate the performances and the applicabilities of the proposed rule and algorithm.