The suffix tree is the most powerful and versatile structure in the string matching. For this structure, the classical construction algorithms in linear time are the Weiner, the McCreight and the Ukkonen algorithm. In this work is presented a review of these construction algorithms and a new one that improves two non functional characteristics: efficiency and usability . This new algorithm reduces the construction time in about 50% (experimentally tested) , the query time and space spent allowing to work with much longer sequences. In this way, the algorithm uses a new design of suffix links structure that provides a major locality between the subtrees (a profit example will be shown). Further more, the resultant algorithm are much more understandable, making it specially easy to modify for resolve concrete problems.