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In the Cu-Zr-Ti ternary system, a new composition zone of bulk metallic glasses (BMGs) formation was discovered, locating at the 55-57 at. pct Cu, 30-31 at. pct Ti and 13-14 at. pct Zr, and near Cu-Ti binary subsystem rather than the Cu-Zr binary. For these alloys, BMG rods of 2 mm in diameter can be fabricated by using copper mould casting. It is expected that these BMG-forming alloys correlate with (L -> CuTi+Cu(2)TiZr+Cu(51)zr(14)) eutectic reaction that the undercooled melt undergoes during solidification. Adopting "3D pinpointing approach", compositional dependence of glass-forming ability (GFA) in Cu(Ni)-Ti-Zr pseudo ternary system was revisited. Optimized BMG-forming composition is located at Cu(50.4)Ni(5.6)Ti(31)Zr(13), with a critical diameter of 6 mm for complete BMG formation. Its GFA is significantly superior to Vit 101 (Cu(47)Ni(8)Ti(34)Zr(11)) previously developed by Caltech group. The effect that the GFA of the ternary base alloy was improved by substitution of Ni for Cu is attributed to a role of retarding the crystallization of Cu(51)Zr(14) intermetallics.