Current profile reproduction has been considered one of the key issues for control and evaluation of a tokamak plasma. Although magnetic measurements exterior to a plasma provide the most reliable data necessary for profile reproduction, the reproducibility from the magnetic measurements is unclear, and the regularization against numerical ill posedness improperly restricts reproducible profiles. To solve the inverse problem, at first, a new method is proposed for the current profile reproduction using a function expansion. Second, with the eigenfunctions in this method, a reproducibility check is analytically formulated. Finally, a new constraint for the plasma interior is derived from the MHD equilibrium equation. In the next step, this constraint must be included to enable reliable reproduction of current profile.