Designing co-amorphous formulations is now recognized as a relevant strategy for improving the bioavailability of low-molecular-weight drugs. In order to determine the most suitable low-molecular-weight excipients for stabilizing the drug in the amorphous state, screening methods were developed mostly using amino acids as co-formers. The present study focused on the analysis of the thermal stability of co-amorphous blends prepared by cryo-milling indomethacin with several amino acids in order to understand the stabilization mechanism of the drug in the amorphous state. Combining low- and mid-frequency Raman investigations has provided information on the relation between the physical properties of the blends and those of the H-bond network of the amorphous drug. This study revealed the surprising capabilities of L-arginine to stiffen the H-bond network in amorphous indomethacin and to drastically improve the stability of its amorphous state. As a consequence, this study suggests that amino acids can be considered as stiffeners of the H-bond network of indomethacin, thereby improving the stability of the amorphous state.