The $B$ mesons are the lightest mesons which can weakly decay to several final states containing baryons. The measurement of the exclusive branching fractions of baryonic $B$ decays, as well as studies on the dynamic of the decay, may allow better understanding of baryon production in $B$ decays and, more generally, hadron fragmentation into baryons. We report about the search for the four-body baryonic decay $B^0\rightarrow p p \bar{p} \bar{p}$, performed on the full dataset of about 471 million $B\bar{B}$ pairs collected with the BaBar detector, which operated at the asymmetric-energy $e^{+}e^{-}$ collider PEP~II, at SLAC National Accelerator Laboratory. No measurement is currently available for this decay channel.