We have investigated the degree of linear polarization and time behaviour of photoluminescence of very small size CdSe nanocrystals under size-selective excitation. At low temperature we observe a luminescence line Stokes-shifted by a few meV and its phonon replica. The degree of linear polarization is positive at short times then becomes negative and remains constant and equal to -15%. The following model is proposed. The exciton state is split by electron-hole exchange interaction into two states with the optically forbidden state at lower energy. Laser light creates excitons in the upper energy state. The luminescence line arises from the lower energy state where excitons have relaxed after a few tens of ps. Recombination is made possible through a phonon assisted virtual transition to the confined B-exciton state. As a result the polarization degree is negative at long times. The value of the exchange energy obtained from the luminescence Stokes shift (8 meV in 40Å-diameter nanocrystals) is much larger than the bulk value (0.1 meV). The enhancement of exchange interaction by quantum confinement and the value of the degree of polarization are in good agreement with theoretical estimates.