  A linear relation for charged-particle emissions is presented starting from
the microscopic mechanism of the radioactive decay. It relates the logarithms
of the decay half-lives with two variables, called $\chi'$ and $\rho'$, which
depend upon the $Q$-values of the outgoing clusters as well as the masses and
charges of the nuclei involved in the decay. This relation explains well all
known cluster decays. It is found to be a generalization of the Geiger-Nuttall
law in $\alpha$ radioactivity and therefore we call it the universal decay law.
Predictions on the most likely emissions of various clusters are presented by
applying the law over the whole nuclear chart. It is seen that the decays of
heavier clusters with non-equal proton and neutron numbers are mostly located
in the trans-lead region. The emissions of clusters with equal protons and
neutrons, like $^{12}$C and $^{16}$O, are possible in some neutron-deficient
nuclei with $Z\geq54$.
