In order to improve the accuracy and efficiency of the inverse kinematics algorithm for general 6R robots, an optimized algorithm was proposed based on symbolic processing and matrix decomposition. The 6 basic inverse kinematics equations were transformed, and symbolic preprocessing was applied to gain 14 inverse kinematics equations without any accumulative errors caused by float point computations. By exploiting the characteristic that 6 equations among them were independent on joint variable 3, the order of the target matrix was reduced from 24 to 16, as while as the number of the included joint variables was increased from 3 to 4. The problem of solving a polynomial of degree 16 was optimized to decomposing a matrix of order 16, and elements with the higher magnitude were selected for calculating the joint variables, so the accuracy was enhanced in a further step. Experiments on general 6R robots show that, the proposed inverse kinematics algorithm can seek 16 real solutions at most with any required accuracy.