We investigate the flavour-changing neutral current decay of the lightest stop into a charm quark and the lightest neutralino and its four-body decay into the lightest neutralino, a down-type quark and a fermion pair. These are the relevant stop search channels in the low-mass region. The SUSY-QCD corrections to the two-body decay have been calculated for the first time and turn out to be sizeable. In the four-body decay both the contributions from diagrams with flavour-changing neutral current couplings and the mass effects of final state bottom quarks and τ leptons have been taken into account, which are not available in the literature so far. The resulting branching ratios are investigated in detail. We find that in either of the decay channels the branching ratios can deviate significantly from 1 in large parts of the allowed parameter range. Taking this into account, the experimental exclusion limits on the stop, which are based on the assumption of branching ratios equal to 1, are considerably weakened. This should be taken into account in future searches for light stops at the next run of the LHC, where the probed low stop mass region will be extended.