NHXM is a new hard X-ray imaging and polarimetric satellite mission characterized by a high spatial and energy resolution over a very broad energy band, from 0.3 to 80(120) keV, together with a sensitive X-ray imaging polarimetric capability. It is based on four identical mirror modules that, for the first time, will extend up to 80(120) keV the fine imaging capability today available only at E<10 keV. At the focus of three telescopes there will be three identical spectro-imaging cameras, at the focus of the fourth an X-ray polarimeter. The addition of a Wide Field X-Ray Monitor, sensitive in the 2-50 keV band, will also permit to detect transient phenomena. NHXM will provide a real breakthrough on a number of hot astrophysical topics, including: i) Black hole census, cosmic evolution and accretion physics; ii) Acceleration mechanism and non-thermal emission; iii) Physics of matter under extreme conditions. A NHXM proposal has been submitted to the ESA 2010 Call for a Cosmic Vision M3 mission.