We investigate a new model of binary fragmentation with inhibition, dr
iven by the white noise. In a broad range of fragmentation probabiliti
es, the power-law spatiotemporal correlations are found to arise due t
o self-organized criticality (SOC). We find in the SOC phase a non-tri
vial power spectrum of the temporal sequence of the fragmentation even
ts. The 1/f behaviour is recovered in the irreversible, near-equilibri
um part of this phase.