We present results of numerical calculations of electronic states of an exciton and a trion (X − ) in a CdTe quantum well at magnetic fields B up to 150 T. The exciton state and the trion states were computed using a variational procedure. We estimated the binding energy of X − in a singlet state with the z-component of angular momentum Lz = 0, as well as the binding energy of the X − in a triplet state with Lz = − . Recent experimental results show that even up to 44 T the binding energy of negative trion in a singlet state is bigger than in a triplet state. We show that at a critical field Bc ≈ 65 T the two binding energies cross and above Bc the binding energy of X − in a triplet state is bigger than in the singlet state.