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 recent the 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 Lagrangians.PACS numbers: 98.80.Es, 98.70.Vc