A balloon borne measurement of the cosmic ray electron spectrum from 10 to 200 GeV is reported in which two new techniques have been used to remove proton background contamination. First, the depth of the spectrometer was more than 25 radiation lengths, the equivalent of more than 2 mean free paths of material, enabling hadronically and electromagnetically induced cascades to be differentiated for a subset of the data. Second, electromagnetic cascade starting points were determined to within + or - 0.1 radiation lengths based upon a calibration with electrons from 5.4 to 18 GeV at the Stanford Linear Accelerator, greatly reducing the chances for a proton to simulate an electron. The resulting spectrum, when fitted with a power law, is quite steep, -3.2 + or - 0.1, but the chi-square fit is marginal. A significantly better fit is achieved assuming a transition region model in which the source spectral index is 2.7 with a break occurring at about 50 GeV.