Ti-based amorphous alloys produced by ultra-rapid melt cooling represent an excellent option as biomaterials because of their mechanical properties and corrosion resistance. However, complete elimination of toxic elements is affecting the glass-forming ability and amorphous structure could be obtained only for thin ribbons or powders that are subsequently processed by powder metallurgy. Amorphous ribbons of special Ti42Zr40Ta3Si15 alloy, which is completely free of any toxic element, were produced by melt spinning, and the thermostability of resulting material was investigated in order to estimate its ability for further heat processing. Isochronal differential scanning calorimetry (DSC) was used to determine transformation points such as glass transition temperature Tg or crystallization temperature Tx. The activation energy for crystallization of amorphous phase was calculated based on Kissinger method, using heating rates ranging between 5 and 20 °C min−1. Amorphous structure of resulting ribbon was evidenced by means of X-rays diffraction (XRD) and high-resolution transmission electron microscopy (HR-TEM). It was determined that amorphous Ti42Zr40Ta3Si15 alloy has a high activation energy for crystallization, similar to other Ti-based amorphous alloys, which provides good thermal stability for subsequent processing, especially by means of powder metallurgy techniques.