The problem of rule extraction from neural networks is NP-hard. This work presents a new technique to extract If-Then-Else rules from linear combinations of DIMLP neural networks. Rules are extracted in polynomial time with respect to the dimensionality of the problem, the number of examples, and the size of the resulting network. Further, the degree of matching between extracted rules and neural network responses is 100%. Linear combinations of DIMLP networks were trained on four data sets related to the public domain. Extracted rules were more accurate than those extracted from C4.5 decision trees on average.