Invented in the 1970s, the Suffix Tree (ST) is a data structure that indexes all substrings of a text in linear space. Although more space demanding than other indexes, the ST remains likely an inspiring index because it represents substrings in a hierarchical tree structure. Along time, STs have acquired a central position in text algorithmics with myriad of algorithms and applications to for instance motif discovery, biological sequence comparison, or text compression. It is well known that different words can lead to the same suffix tree structure with different labels. Moreover, the properties of STs prevent all tree structures from being STs. Even the suffix links, which play a key role in efficient construction algorithms and many applications, are not sufficient to discriminate the suffix trees of distinct words. The question of recognising which trees can be STs has been raised and termed Reverse Engineering on STs. For the case where a tree is given with potential suffix links, a seminal work provides a linear time solution only for binary alphabets. Here, we also investigate the Reverse Engineering problem on ST with links and exhibit a novel approach and algorithm. Hopefully, this new suffix tree characterisation makes up a valuable step towards a better understanding of suffix tree combinatorics.