Some secondary or beta relaxations in glass-forming materials involve molecular motions that bear strong resemblance to the primitive ct relaxations of the coupling model, although the two are not identical. For these beta relaxations, at the glass transition temperature T-g the relaxation time tau(beta)(T-g) is expected to be shorter than but not too different in order of magnitude from tau(0)(T-g), the primitive alpha-relaxation time at T-g. The latter can be calculated by the coupling model from the relaxation time tau(alpha)(T-g), the exponent (1-n) of the Kohlrausch-Williams-Watts (KWW) correlation function exp[-(t/tau(alpha))(1-n)], and the experimental crossover time, t(c)approximate to 2ps, of the alpha relaxation. From experimental data of beta and a relaxations in a variety of glass-forming materials, it is found that tau(beta)(T-g) and tau(o)(T-g) are close to each other in order of magnitude as anticipated. The results indicate these beta relaxations indeed bear some close relation to the corresponding primitive alpha relaxation, although they are not the same process. Since the relaxation times of the majority of these beta relaxations have the Arrhenius temperature dependence, tau(beta)(T) = tau(beta proportional to) exp(E-beta/RT), where tau(beta proportional to) is of the order of 10(-13)-10(-16) s, knowing, approximately, the value of tau(beta)(T) at one temperature T-g means the location of the beta relaxation in the relaxation map can be roughly determined from the alpha relaxation. The findings can be restated as the empirical result : there exists a strong correlation between the value of log[tau(beta)(T-g)] and the KWW exponent (1-n) of the alpha relaxation in many glass-formers. A smaller KWW exponent of the alpha relaxation corresponds to shorter tau(beta)(T-g) or smaller log[tau(beta)(T-g)]. This remarkable cross correlation between the ct relaxation and the beta relaxation should be of interest for any model or theory of molecular dynamics of glass formers.