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The present invention provides a Cu-Be based amorphous alloy comprising an amorphous phase of 50% or more by volume fraction. This alloy has a composition represented by the following Formula : Cu 100-a-b Be a (Zr 1-x-yHfx Ti y) b. In the formula, "a" and "b" represent atomic percentages which are 0 < a = 20 and 20 = b = 40, and "x" and "y" represent atomic fractions which are 0 = x = 1 and 0 = y = 0.8. The alloy may contain a small amount of one or more elements selected from the group consisting of Fe, Cr, Mn, Ni, Co, Nb, Mo, W, Sn, Al, Ta and rare-earth elements and/or the group consisting of Ag, Pd, Pt and Au. The alloy has a wide supercooled-liquid temperature range and a large reduced glass transition temperature (Tg/Tm) to achieve a high thermal stability against crystallization or a high glass-forming ability.