Fifty-six amber mutations of the beta-galactosidase gene of Escherichia coli were suppressed by crossing into a stock containing the supD suppressor gene. The resultant enzymes, differing only in the position of the inserted serine, were tested for stability at 57 C. Most of the suppressed enzymes were either as stable to heat as the normal enzyme or very unstable. Tests of enzymes produced by the action of other suppressors showed that the degree of stability was characteristic of a particular position in the polypeptide chain of the amino acid substitution and independent of the amino acid inserted. The mutations were placed in linear order in the gene by deletion mapping and three-point linkage tests. The consequent order of the serine substitutions disclosed an alternating pattern of stable and unstable regions over the amino-terminal two-thirds of the enzyme; the carboxy-terminal third of the enzyme was generally unstable. Considerations of coding relations and enzyme structure suggested that serine and glutamine suppression usually result in a change in the hydrophilic nature of the side chains on the outside of the enzyme molecule. It was shown that the potentially unstable regions of the enzyme are probably not indicative of stretches of alpha-helix or of sites of association. The apparent position of the substrate binding sites was correlated with the location of some of the potentially unstable regions, which may mark the parts of the polypeptide chain in proximity with the substrate.