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An internally thermalized dark matter (DM) with only gravitational interaction with the standard model (SM) particles at low temperatures, may undergo number-changing self-scatterings in the early Universe, eventually freezing out to the observed DM abundance. If these reactions, such as a $3 \rightarrow 2$ process, take place when the DM is non-relativistic, DM cannibalizes itself to cool much slower than standard non-relativistic matter during the cannibal phase. As shown in earlier studies, if the cannibal phase takes place during the matter-dominated epoch, there are very strong constraints from structure formation. Considering scenarios in which the cannibal phase freezes out in the radiation-dominated epoch instead, we show that cannibal DM decoupled from the SM can be viable, consistent with all present cosmological constraints. To this end, we solve the coupled evolution equations of the DM temperature and density, and determine its abundance for different DM self-couplings. We then evaluate the constraints on these parameters from the cosmic-microwave background power spectrum, the big-bang nucleosynthesis limits on the relativistic degrees of freedom, the Lyman-$α$ limits on the DM free-streaming length and the theoretical upper bound on the $3 \rightarrow 2$ annihilation rate from $S-$matrix unitarity. We find that depending upon the DM self-couplings, a scalar cannibal DM with mass in the range of around 80 eV to 700 TeV can make up the observed DM density and satisfy all the constraints, when the initial DM temperature ($T_{\rm DM}$) is lower than the SM one ($T_{\rm SM}$), with $T_{\rm SM}/9100 \lesssim T_{\rm DM} \lesssim \,T_{\rm SM}/1.1$.