  We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the
$\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In
this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in
terms of on-shell $\mathcal {N}=2$ harmonic superfields. Such an approach
provides a convenient tool of constructing the manifestly $\mathcal{N}=4$
supersymmetric invariants and further rewriting them in $\mathcal{N}= 2$
harmonic superspace. In particular, we present $\mathcal{N}=4$ superfield form
of the leading term in the $\mathcal{N}=4$ SYM effective action which was known
previously in $\mathcal{N}=2$ superspace formulation.
