  Proceeding from a nonlinear realization of the most general N=4, d=1
superconformal symmetry, associated with the supergroup D(2,1;alpha), we
construct a new model of nonrelativistic N=4 superconformal mechanics. In the
bosonic sector it combines the worldline dilaton with the fields parametrizing
the R-symmetry coset S^2 ~ SU(2)/U(1). We present invariant off-shell N=4 and
N=2 superfield actions for this system and show the existence of an independent
N=4 superconformal invariant which extends the dilaton potential. The extended
supersymmetry requires this potential to be accompanied by a d=1 WZW term on
S^2. We study the classical dynamics of the bosonic action and the geometry of
its sigma-model part. It turns out that the relevant target space is a cone
over S^2 for any non-zero alpha \neq \pm 1/2. The constructed model is expected
to be related to the `relativistic' N=4 mechanics of the AdS_2 times S^2
superparticle via a nonlinear transformation of the fields and the time
variable.
