[en] Waves with frequencies near the harmonics of the proton-cyclotron frequency, and propagating almost transverse to the ambient magnetic field, can become unstable by hot protons having an anti-loss cone (ALC) distribution function. The maximum growth rates increase with an increase in anti-loss cone index, ratio of the temperatures of trapped to missing protons, and with a decrease in βHsub(H) (βsub(H) being the ratio of transverse thermal pressure of protons to magnetic field pressure). The growth rates are typically in the range 0.01-1.0 Ω, where Ω is the proton-cyclotron frequency. This instability may be relevant to the observations of EHC waves on auroral field lines (Kintner, 1979), ULF waves in the day-side magnetosphere (Perraut et al., 1978) and the low-frequency part of the electric field spectrum (from 5 Hz to 20 Hz) in the region upstream of the bow-shock (Gurnett et al., 1979). (orig.)