The possible adverse influence of the steps in a multiple attribute decision making method, including normalization of the decision matrix and calculation of the attributes weights, on the reasonableness of the method is analyzed. To eliminate the bad effects caused by above mentioned steps, a new multiple attribute decision making method is proposed. The method calculats attributes weights based on a group decision making mode. The attributes weights are gained by aggregating those attributes weights given by experts whose judgements are consistent. Then by defining the relative dominance relations between schemes upon different kinds of attributes whose values are real numbers, interval numbers or linguistic values, a judgment matrix is constructed. On that basis, a linear objective programming model is established to calculate the utility value of each scheme, which is used in scheme evaluation and sorting. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed multiple attribute decision making method.