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The glass-forming ability and properties of Ni-based Ni-Fe-B-Si-Ta bulk metallic glasses are explored in this work. The alloy compositions are determined by using a combination of the cluster line approach, the multi-alloying strategy and the substitutions of similar elements. Bulk metallic glasses with diameters of 3 mm take shape at compositions formulated under the cluster-plus-glue-atom model [M(9)B]B similar to[(Ni(1-x)Fe(x))(7.71)(Si(0.66)Ta(0.34))(1.29)B]B(0.94)=(Ni(1-x)Fe(x))( 70.5)B(17.7)Si(7.8)Ta(4), x=0.35-0.45, where the bracketed part is the cluster and the unbracketed part is the glue atoms. These alloys exhibit good magnetic properties. The maximum I(s) is found in the (Ni(0.55)Fe(0.45))(70.5)B(17.7)Si(7.8)Ta(4) alloy which reaches 0.51 T, with its H(c) as low as 8.5 A/m. Interestingly, these alloys display dual glass transitions at (Ni(0.65)Fe(0.35))(70.5)B(17.7)Si(7.8)Ta(4), (Ni(0.60)Fe(0.4))(70.5)B(17.7)Si(7.8)Ta(4) and (Ni(0.55)Fe(0.45))(70.5)B(17.7)Si(7.8)Ta(4) as unveiled by Temperature-Modulated Differential Scanning Calorimetry.