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We have measured electron spin flip transition frequencies in the $X2\Sigma +$ ground state of YbF using laser-rf double resonance spectroscopy. This technique leads to significant improvement in accuracy compared with our previous Doppler-free laser measurements of YbFs spin-rotation/hyperfine $structure.1$ YbF might be expected to resemble the alkaline earth fluorides, but we find its spin-rotation structure to be anomalous. Apart from its interest as a "single electron molecule", YbF is expected to be an extremely sensitive system with which to search for a permanent electric dipole moment (edm) of the $electron.2$ The electron edm has important consequences for elementary particle physics. In particular, many extensions to the Standard Model of elementary particle physics predict the electron edm to be large enough to be measured in a sensitive experiment. We discuss the prospects for such a measurement in light of our recent results.