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We present Mg isotope ratios in four red giants of the globular cluster M13 and one red giant of the globular cluster M71 based on high-resolution, high signal-to-noise ratio spectra obtained with HDS on the Subaru Telescope. We confirm earlier results by Shetrone that for M13 the ratio varies from ²⁵Mg+²⁶Mg/²⁴Mg≃1 in stars with the highest Al abundance to ²⁵Mg+²⁶Mg/²⁴Mg≃0.2 in stars with the lowest Al abundance. However, we separate the contributions of all three isotopes and find a considerable spread in the ratio ²⁴Mg:²⁵Mg:²⁶Mg, with values ranging from 48:13:39 to 78:11:11. As in NGC 6752, we find a positive correlation between ²⁶Mg and Al, an anticorrelation between ²⁴Mg and Al, and no correlation between ²⁵Mg and Al. In M71, our one star has a Mg isotope ratio of 70:13:17. For both clusters, even the lowest ratios of ²⁵Mg/²⁴Mg and ²⁶Mg/²⁴Mg exceed those observed in field stars at the same metallicity, a result also found in NGC 6752. The contribution of ²⁵Mg to the total Mg abundance is constant within a given cluster and between clusters with ²⁵Mg/²⁴Mg+²⁵Mg+²⁶Mg≃0.13. For M13 and NGC 6752, the ranges of the Mg isotope ratios are similar and both clusters show the same correlations between Al and Mg isotopes, suggesting that the same process is responsible for the abundance variations in these clusters. While existing models fail to reproduce all the observed abundances, we continue to favor the scenario in which two generations of asymptotic giant branch (AGB) stars produce the observed abundances. A first generation of metal-poor AGB stars pollutes the entire cluster and is responsible for the large ratios of ²⁵Mg/²⁴Mg and ²⁶Mg/²⁴Mg observed in cluster stars with compositions identical to field stars at the same metallicity. Differing degrees of pollution by a second generation of AGB stars of the same metallicity as the cluster provides the star-to-star scatter in Mg isotope ratios.