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The KV-homology theory is a new framework which yields interesting properties of lagrangian foliations. This short note is devoted to relationships between the KV-homology and the KV-cohomology of a lagrangian foliation. Let us denote by ${}_F$ (resp. $V^F$) the KV-algebra (resp. the space of basic functions) of a lagrangian foliation F. We show that there exists a pairing of cohomology and homology to $V^F$. That is to say, there is a bilinear map $H^q{(}_F,V^F)\times H_q{(}_F,V^F)\to V^F$, which is invariant under F-preserving symplectic diffeomorphisms....