The angular momentum projected shell model (PSM) is applied to the nucleus
84Rb. The results of theoretical calculations about the positive-parity yrast band with configuration
πg9/2νg9/2 and the negative-parity yrast band with configuration
π(p3/2,f5/2)νg9/2 are compared with experimental data. The interpretation within the projected shell model shows that the signature inversion displayed in the positive-parity yrast band in this nucleus is a signal of a substantial quadrupole shape change with increasing spin where the nucleus evolves from a prolate shape at low spin through a triaxial shape to an oblate shape at high spin. In addition, we also specify the nuclear shape for these two bands.