Summary: Let \(A\) be a regular multiplier Hopf algebra and \(R\) be an \(A\)-bicomodule algebra. The authors define an \(A\)-bicomodule bialgebra and construct a non-trivial multiplier Hopf algebra on \(R\otimes A\) called an L-R smash coproduct which is the dual of the L-R smash product. The integrals and \(*\)-operators on the L-R smash coproduct are also obtained.