  We describe a new basis of the ring of quasi-symmetric coinvariants, which is
stable by the natural reversal of the set of variables. The indexing set is the
set of triangulations of a regular polygon, instead of the set of Dyck paths
used for the known basis. On d\'{e}crit une nouvelle base de l'alg\`{e}bre des
coinvariants quasi-sym\'{e}triques, qui est stable par l'involution naturelle
et index\'{e}e par les triangulations d'un polygone r\'{e}gulier.
