The traditional AVL (Adelson-Velskii and Landis) tree programming has been faced with the problem of too much code, complex process and high adjusting ratio. To solve these problems, a unified rebalancing method was developed and a generalized AVL (AVL-N) tree was defined. The unified rebalancing method automatically classifies the type of the unbalanced node in AVL tree and uses a new way to adjust the tree shape without using standard rotations. AVL-N tree with relaxed balance allows the height difference between the right sub-tree and left sub-tree doesn't exceed N(N ≥ 1). When insertions and deletions have been performed in AVL-N tree, the height difference between the right sub-tree and left sub-tree of some nodes may be higher than N. At that time the unified rebalancing would be applied to rearrange the unbalanced node's descendants. The simulation results indicate that the adjusting ratio of AVL-N tree reduced significantly with N increasing, it is less than 4% for N=5 and less than 0.1% for N=13. The adjusting ratio of AVL-N tree is far below other classic data structures, such as red-black tree, and allows for a greater degree of concurrency than the original proposal.