In genetic programming (GP), evolving tree nodes separately would reduce the huge solution space. However, tree nodes are highly interdependent with respect to their fitness. In this paper, we propose a new GP framework, namely, instruction-matrix (IM)-based GP (IMGP), to handle their interactions. IMGP maintains an IM to evolve tree nodes and subtrees separately. IMGP extracts program trees from an IM and updates the IM with the information of the extracted program trees. As the IM actually keeps most of the information of the schemata of GP and evolves the schemata directly, IMGP is effective and efficient. Our experimental results on benchmark problems have verified that IMGP is not only better than those of canonical GP in terms of the qualities of the solutions and the number of program evaluations, but they are also better than some of the related GP algorithms. IMGP can also be used to evolve programs for classification problems. The classifiers obtained have higher classification accuracies than four other GP classification algorithms on four benchmark classification problems. The testing errors are also comparable to or better than those obtained with well-known classifiers. Furthermore, an extended version, called condition matrix for rule learning, has been used successfully to handle multiclass classification problems.