We demonstrate spin injection and detection in single wall carbon nanotubes using a 4-terminal, non-local geometry. This measurement geometry completely separates the charge and spin circuits. Hence all spurious magnetoresistance effects are eliminated and the measured signal is due to spin accumulation only. Combining our results with a theoretical model, we deduce a spin polarization at the contacts of approximately 25 %. We show that the magnetoresistance changes measured in the conventional two-terminal geometry are dominated by effects not related to spin accumulation.