We propose a self-stabilizing synchronization technique, called the {\it Global Rooted Synchronization}, that synchronizes processors in a tree network. This synchronizer can be used as a compiler to convert a synchronous protocol $P$ for tree networks into a self-stabilizing version of $P$ for tree networks. The synchronizer requires only $O(1)$ memory (other than the memory needed to maintain the tree) at each node regardless of the size of the network, stabilizes in $O(h)$ time, where $h$ is the height of the tree, and does not invoke any global operations. Several applications of this technique are presented, such as the distributed clock synchronization and global calculus computation--each being efficient both in time and space complexity compared to the previous results.