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In this paper, for an arbitrary regular biordered setE, by using biorder-isomorphisms between the ?-ideals ofE, we construct a fundamental regular semigroupWE called NH-semigroup ofE, whose idempotent biordered set is isomorphic toE. We prove further thatWE can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroupSwith the idempotent biordered set isomorphic toE, there exists a homomorphism fromStoWE whose kernel is the greatest idempotent-separating congruence onSand the image is a full symmetric subsemigroup ofWE. Moreover, whenEis a biordered set of a semilatticeE0,WE is isomorphic to the Munn-semigroup; and whenEis the biordered set of a bandB,WE is isomorphic to the Hall-semigroupWB. [ABSTRACT FROM AUTHOR]