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A new method has been developed for measuring the magnitude of nuclear spin polarization of a secondary, radioactive beam by making a pulsed magnetic field measurement that does not require advance knowledge of the nuclide's magnetic moment. Using a standard β NMR apparatus, a magnetic double ratio is determined from the counting rates in 0° and 180° β detectors for magnetic field on and off conditions. This ratio provides direct information on the induced spin polarization of a radioactive beam. A demonstration of the method was performed using spin polarized 12B nuclei produced by fragmentation of an 80 MeV/nucleon 18O beam in a Nb target.