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The BaR-SPOrt experiment is designed to measure the E-mode power spectrum of the Cosmic Microwave Background Polarization (CMBP) in the multipole range 50 < l < 1000. In the current configuration at 32 GHz it can explore up to l = 400. Recent low frequency observations of the target region show that the synchrotron emission should not contamine the CMBP already at 32 GHz. A 6-month observation of a 6° × 6° sky area during the polar night, in ideal environmental conditions, will allow the Italian-French collaboration to both measure the E–mode power spectrum with appropriate sensitivity and perform important tests of the anomalous dust emission. The BaR-SPOrt 32 GHz instrument, now under test and ready for operations by Spring 2005, is proposed for 1–2 years Winter operations at Dome C.