Electromagnetic instabilities in a plasma with a hollow q-profile are investigated. The tearing mode is found to be unstable even in the absence of external driving magnetic energy and can manifest itself either as the 'binary-tearing' mode with two peaks near the rational surfaces or as the 'centred' mode. The centred mode has no classical analogue and a higher growth rate than the 'double-tearing' limit. The double-tearing mode of Pritchett et al. is a special case of a binary-tearing mode.