  We investigate the quantum phase transitions in the frustrated
antiferromagnetic Heisenberg model for $\rm SrCu_2(BO_3)_2$ by using the series
expansion method. It is found that a novel spin-gap phase, which is
adiabatically connected to the plaquette-singlet phase, exists between the
dimer and the magnetically ordered phases known so far. When the ratio of the
competing exchange couplings $\alpha(=J'/J)$ is varied, this spin-gap phase
exhibits the first- (second-) order quantum phase transition to the dimer (the
magnetically ordered) phase at the critical point $\alpha_{c1}=0.677(2)$
($\alpha_{c2}=0.86(1)$). Our results shed light on some controversial arguments
about the nature of the quantum phase transitions in this model.
