abstract: Bijections between nbc-basis of Orlik Solomom Algebra, chambers and, more recently, minimal complex of a complexified real arrangement have been studied by many authors. In this talk we illustrate a very particular bijiection in the case of supersolvable arrangements. This bijection has a very handy description that tourn out to be useful to study the (co)-homology of the Milnor Fibre for such arrangements and to give a direct description of a bijiection introduced by Barcelo and Goupil, between elements of the symmetric group and nbc-basis of OS Algebra of Braid arrangement.