  We propose a unified superfield formulation of N=4 off-shell supermultiplets
in one spacetime dimension using the standard N=4 superspace. The main idea of
our approach is a "gluing" together of two linear supermultiplets along their
fermions. The functions defining such a gluing obey a system of equations. Each
solution of this system provides a new supermultiplet, linear or nonlinear,
modulo equivalence transformations. In such a way we reproduce all known linear
and nonlinear N=4, d=1 supermultiplets and propose some new ones. Particularly
interesting is an explicit construction of nonlinear N=4 hypermultiplets.
