We study wave emissions, in the frequency range from above the lower hybrid frequency up to the plasma frequency, observed during one of the Cluster crossings of a high-beta exterior cusp region on 4 March 2003. Waves are localized near narrow current sheets with a thickness a few times the ion inertial length; currents are strong, of the order of 0.1-0.5μA/m² (0.1-0.5mA/m² when mapped to ionosphere). The high frequency part of the waves, frequencies above the electron-cyclotron frequency, is analyzed in more detail. These high frequency waves can be broad-band, can have spectral peaks at the plasma frequency or spectral peaks at frequencies below the plasma frequency. The strongest wave emissions usually have a spectral peak near the plasma frequency. The wave emission intensity and spectral character change on a very short time scale, of the order of 1s. The wave emissions with strong spectral peaks near the plasma frequency are usually seen on the edges of the narrow current sheets. The most probable generation mechanism of high frequency waves are electron beams via bump-on-tail or electron two-stream instability. Buneman and ion-acoustic instability can be excluded as a possible generation mechanism of waves. We suggest that high frequency waves are generated by electron beams propagating along the separatrices of the reconnection region.