  In this paper, extending the idea presented by M. Takeuchi in [13], we
introduce the notion of partial matched pair $(H,L)$ involving the concepts of
partial action and partial coaction between two Hopf algebras $H$ and $L$.
Furthermore, we present necessary conditions for the corresponding bismash
product $L\# H$ to generate a new Hopf algebra and, as illustration, a family
of examples is provided.
