Cholesky decomposition (CD) of the two-electron integrals is an established numerical technique to evaluate the molecular two-electron integral matrix. In the past years, development on how to systematical improve accuracy without method bias has been lead by the Lindh group through the development of atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Atomic CD set can be obtained from the Cholesky decomposition of the atomic integral basis set. To limit the size of the auxiliary basis set, atomic compact CD set is developed thru the removal of linear dependence of the primitives via subsequent CD. The accuracy of these methods can be further improved via an explicit correction of the one-centered two-electron integrals, which is the main object of this research. The accuracy of aCD and acCD methods is controlled by a single parameter, tau, which determines the size of the auxiliary basis set. Correcting the one-centered two-electron integrals directly is expected to achieve acceptable accuracy with a higher tau threshold effectively decreasing the necessary auxiliary basis set size.