Using The Hubble Space Telescope's Space Telescope Imaging Spectrograph HST's STIS, observations of the OIII emission from the narrow-line region (NLR) of NGC 4151 were obtained and radial velocities determined. Five orbits of HST time were used to obtain spectra at five parallel slit configurations, at a position angle of 58 degrees, with spatial resolution 0.2 arcseconds across and 0.1 arcseconds along each slit. A spectral resolving power of ~ 9,000 with the G430M grating gave velocity measurements accurate to ~ 34 km/s. A kinematic model was generated to match the radial velocities, for comparison to previous kinematic models of biconical radial outflow developed for low-dispersion spectra at two slit positions. The new high-resolution spectra permit the measurement of accurate velocity dispersions for each radial-velocity component. The full-width at half-maximum (FWHM) reaches a maximum of 1000 km/s near the nucleus, and generally decreases with increasing distance to about 100 km/s in the extended narrow-line region (ENLR), starting at about 6 arcseconds from the nucleus. In addition to the bright emission knots, which generally fit our model, there are faint high velocity clouds which do not fit the biconical outflow pattern of our kinematic model. These faint clouds occur at the turnover points of the outflowing bright clouds. We suggest possible scenarios that could explain these rogue clouds: (1) backflow resulting from shocks and (2) outflow outside of the bicones, although the latter does not explain how the knots are ionized and accelerated. A comparison of our observations with a high-resolution radio map shows that there is no evidence that the kinematics of the NLR clouds are affected by the radio lobes that comprise the inner jet.