  For the first time connection between the pulsation and modulation properties
of RR Lyrae stars has been detected. Based on the available data it is found
that the possible range of the modulation frequencies, i.e, the possible
maximum value of the modulation frequency depends on the pulsation frequency.
Short period variables (P < 0.4 d) can have modulation period as short as some
days, while longer period variables (P > 0.6 d) always exhibit modulation with
P_mod > 20 d. We interpret this tendency with the equality of the modulation
period with the surface rotation period, because similar distribution of the
rotational periods is expected if an upper limit of the total angular momentum
of stars leaving the RGB exists. The distribution of the projected rotational
velocities of red and blue horizontal branch stars at different temperatures
shows a similar behaviour as v_rot derived for RR Lyrae stars from their
modulation periods. This common behaviour gives reason to identify the
modulation period with the rotational period of the modulated RR Lyrae stars.
