The Universal Decay Law (UDL) formula for the alpha and cluster decays is extended to include the effects of the angular momentum and isospin. The parameters for all formulas are obtained by fitting to available experimental data. We also evaluated the uncertainty of the parameters as well as the uncertainties of predictions of the formulas. The rms values are computed and the best rms among them is obtained for the formula including both the angular momentum and isospin terms. The modified UDL formula is applied to get the half-lives of cluster and alpha decays of nuclei. Branching ratios (alpha/cluster) are calculated and compared with experimental ones. The half-lives for heavier cluster decays are obtained by using UDL and new UDL formulas.