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Near the melting transition the bending elastic constant, $\kappa$, anemergent property of double-stranded DNA (dsDNA), is shown not to follow therod-like scaling for small length $N$. The reduction in $\kappa$ withtemperature is determined by the denatured bubbles for a continuous transition,e.g., when the two strands are gaussian, but by the broken bonds near the openend in a Y-like configuration for a first-order transition as for strands withexcluded volume interactions. In the latter case, a lever rule is operationalimplying a phase coexistence although dsDNA is known to be a single phase.

Softening of DNA near Melting as Disappearance of an Emergent Property