The influence of dispersive magnetic permeability on spatiotemporal instability (STI) in metamaterials is identified based on the Drude model. In the case of co-existence of cubic nonlinearity,pseudo-fifth-order nonlinearity and self-steepening,a generic expression for instability growth rate is derived. It is found that in the negative-index region,the pseudo-fifth-order nonlinearity increases the range of spectrum and the gain value of STI for the case of self-focusing material while it do opposite for the case of self-defocusing material,which are different from the results in ordinary materials,in the negative-index region,the pseudo-fifth-order nonlinearity will suppress the emergence of STI for the case of self-focusing material,which exhibits the same features for the case of ordinary material. In any way the self-steepening in metamaterials always tends to suppresses appearance of STI regardless of its sign.