We propose a polarization-independent optical isolator that does not use walk-off between the two orthogonal polarizations. The design is based on two Faraday rotators in combination with two half-wave plates in a closed, Sagnac-interferometer-like, configuration. An experimental prototype is tested successfully under variation of the input light polarization state with isolation level between 43 dB and 50 dB for all input polarizations (linear, circular, or elliptical).