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The Italian New Hard X-ray Mission (NHXM) has been designed to provide a real breakthrough on a number of hot astrophysical issues that includes: black holes census, the physics of accretion, the particle acceleration mechanisms, the effects of radiative transfer in highly magnetized plasmas and strong gravitational fields. NHXM is an evolution of the HEXIT-Sat concept and it combines fine imaging capability up to 80 keV, today available only at E<10 keV, with sensitive photoelectric imaging polarimetry. It consists of four identical mirrors, with a 10 m focal length, achieved after launch by means of a deployable structure. Three of the four telescopes will have at their focus identical spectral-imaging cameras, while X-ray imaging polarimetric cameras will be placed at the focus of the fourth. In order to ensure a low and stable background, NHXM will be placed in a low Earth equatorial orbit. In this paper we provide an overall description of this mission that is currently in phase B.