Catalysts are not actually catalysts if they cannot be used for an indefinite number of times. We establish a resource theory of one-shot catalytic randomness and show that uncorrelatedness is being consumed in randomness-utilizing processes. We give the mutual information an operational meaning as a measure of already extracted entropy from a catalyst and identify the maximally extractable entropy for arbitrary catalyst. This identification leads to the definition of the catalytic entropy and its R\'{e}nyi generalizations. We already give give an operational meaning to the partial transpose of bipartite unitary operator; a bipartite unitary operator whose partial transpose is also unitary is a catalysis unitary. Next, we show that explicit treatment of correlation of catalyst opens up multiple applications including infinite multi-party catalysis and randomness deposit into catalyst.