Convection in the form of thermal Rossby waves is studied in the low Prandtl number regime. An anomalous Eckhaus instability is found in the range between 10−3and 10−2for a moderately strong Coriolis parameter, where no supercritical stable solution can exist near the onset. Numerical results for higher Rayleigh numbers show detachment of the stability limit from the neutral curve, shrinkage and distortion of the stable region, and the onset of a second sideband mode of instability, which is characterized by a maximum growth rate at a finite modulation parameter. The new mode is more pronounced at higher Rayleigh numbers, and appears to destabilize all spatially periodic waves for the whole supercritical band for all Prandtl numbers below the anomalous range. ©1995 American Institute of Physics.