The spectral range of the Hinode EIS (EUV Imaging Spectrometer) instrument is 170-211 Å and 245-291 Å lines emitted by low-energy levels in highly ionized Mn, Fe, Co, and Ni, as well as the very energetic 1s2s3S1-1s2p3P2 transition in Fe XXV, appear in the EIS range. In this paper, we investigate the use of these lines for detecting the presence of nonthermal, high-energy electrons in flares. We first calculate line fluxes among the various lines expected in the EIS range, assuming that the electron velocity distribution is strictly Maxwellian. Then, we calculate line fluxes using a velocity distribution composed of a Maxwellian distribution plus an additional population of electrons with a temperature of 10 keV (1.2 × 108 K) providing 1%, 2%, 4%, 7%, and 10% of the total free electrons. The calculations indicate that flux ratios between the highly excited Fe XXV line and lines originating in low-lying levels of other highly ionized ions in the EIS range could shed light on the electron velocity distribution in hot flare plasmas.