The purpose of my talk is the investigation of the finite dimensional situation ; in that case one deals with multiplicative partial isometries which generates finite dimensional C*-quantum groupoids, these last objects where defined by G.Boehm, F.Nill and C.Schlachanayi who made a talk on this subject in your previous Congress ( Nov. 1995) using an other terminology (weak Hopf algebras). In particular these multiplicative partial isometries have in the regular situation a canonical irreducible decomposition, in that case there is a nice multiplicative property for the canonical conditional expectation on the intersection of the two C*-quantum groupoids it generates. This multiplicativity leads to a nice characterisation of C*-quantum groupoids in duality in the Kac case.