  We present a model independent method of reconstructing the Lagrangian for
the k-essence field driving the present acceleration of the universe. We
consider the simplest k-essence model for which the potential is constant.
Later we use three parametrizations for the Hubble parameter $H(z)$, consistent
with the recent SN1a data, to yield the Lagrangian $F$. Our reconstruction
program does not generate any physically realistic Lagrangian for models that
allow phantom crossing, whereas models without phantom crossing, yield well
behaved Lagrangian.
