A passive neutron rem counter using a CR39 SSNTD coupled with a boron converter has been developed. The rem counter is a polythene sphere with cadmium and lead insets, designed to have a response function proportional to the fluence to ambient dose equivalent conversion coefficients, H*(10)/Φ, for energies ranging from thermal up to 1 GeV. At its centre is a thermal neutron detector made of a CR39 SSNTD coupled with an enriched boron neutron converter. The rem counter was first calibrated at CERN and at the Politecnico di Milano, and then tested in high-energy neutron fields at GSI, Darmstadt, Germany and at the CERF facility at CERN. Its most important features are a very high neutron sensitivity and conversely a complete insensitivity to gamma radiation.