The potential curves of the ground states of the TlF molecule and TlF- anion are ab initio calculated by the relativistic coupled clusters method using a generalized relativistic pseudopotential. The corresponding spectroscopic parameters are calculated and it is shown that TlF- is stable in the lowest vibrational states. The information obtained is necessary for preparing a new series of experiments aimed at searching for CP-noninvariant effects in nucleon-nucleon interactions on the basis of the TlF molecule.