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Intersystem lines of O IV near 1400 \AA\ have long been used as electron density diagnostics for solar plasmas at temperatures of around 160,000 K. In addition, however, several allowed lines of O IV near 1340 \AA\ should become visible in conditions of high plasma electron number density ($N_{e} > 10^{12}$ cm$^{-3}$), such as during a solar flare. We present observations of the 1340 \AA\ and 1400 \AA\ regions of the solar spectrum for two solar flares, obtained by the S082B spectrograph on board Skylab. We examine three candidate lines for allowed O IV in the flare spectra which occur at the correct wavelengths, but show that two of these are actually blends dominated by resonantly excited molecular lines of H$_{2}$. The third candidate line, at 1343.51 \AA, we identify as the O IV allowed line. We present the density and temperature sensitivity of the ratio of allowed and intersystem O IV lines $R = I(1343.51$ \AA)/$I(1407.39$ \AA). The 1343.51 \AA\ line is clearly present in the first solar flare spectrum, and the ratio value implies an electron density of log $N_{e}$ = 12.6. The second flare has a much weaker 1343.51 \AA\ profile, but again the ratio value implies a high electron density. Both these electron density values are in good agreement with estimates for each flare from independent diagnostic ratios. The simple presence alone of a clearly observed O IV 1343.51 \AA\ emission line implies an electron density greater than 10$^{12}$ cm$^{-3}$.
