A new method of weighting that realizes equiredundancy design is introduced, and its convergence is better than the method introduced by Koch. However, if Koch's method is modified, it gives the best results compared to the others. Furthermore, it is shown that balanced weights depend only on the positions of observations and not on the initial weights. Lf the equiredundancy design is taken into consideration in the generalized form of maximum likelihood estimation (M-estimation), the finite sample breakdown point (FSBP) (or reliability) increases. This problem has been studied using a coordinate transformation simulation. After obtaining the balanced weights, which provide the equiredundancy, they are used as the pseudoweights of observations in M-estimation. This is called the equiredundancy-designed generalized M-estimation (GM-estimation). In addition, another GM-estimation is developed by balancing the partial redundancy numbers at every step of the reweighted aid iterated least-squares solution of M-estimation. This is called the GM-estimation with balanced case. Both methods have the same FSBP. Using both methods of GM-estimation in the robustifying conventional outlier detection procedures, such as the method of Baarda or Pope, the new robustifying outlier detection procedures are obtained with a higher FSBP.