  The method of nonlinear realizations is used to clarify some conceptual and
technical issues related to the Schwarzian mechanics. It is shown that the
Schwarzian derivative arises naturally, if one applies the method to SL(2,R)
times R group and decides to keep the number of the independent Goldstone
fields to a minimum. The Schwarzian derivative is linked to the invariant
Maurer-Cartan one-forms, which make its SL(2,R)-invariance manifest. A
Lagrangian formulation for a variant of the Schwarzian mechanics studied
recently in [Nucl. Phys. B 936 (2018) 661] is built and its geometric
description in terms of 4d metric of the ultrahyperbolic signature is given.
