Display omitted •The two-component transformation inclusive contraction (TIC) scheme is introduced.•The unitarized Douglas–Kroll (uDK) method is also introduced for TIC.•The TIC scheme produced highly accurate results for systems involving heavy atoms.•The uDK method was demonstrated to perform marginally better than conventional DK. The incorporation of a two-component transformation into the contraction coefficients of basis functions is suggested. Such a contraction, referred to as “two-component transformation inclusive contraction (TIC)”, effectively eliminates the computational cost associated with the two-component transformation and can be readily implemented into conventional quantum chemistry programs. TIC was verified through numerical calculations using the second- and third-order unitarized Douglas–Kroll method, which is newly derived for the validation of TIC, and the infinite-order two-component method. The numerical validation results suggested that TIC could sufficiently reproduce the results of primitive basis sets for both atoms and molecules.