We present an analytical based proof for the consistency between a new model, proposed by Zhou et al. [Phys. Rev. Lett. 82 (1999) 4560], of the double-stranded DNA (dsDNA) and the well accepted wormlike rod chain (WLRC) model in the regime around the undistorted B-form. The relationship between the Zhou, Zhang, and Ou-Yang (ZZO) model and a recent proposed asymmetric elastic ribbon model is also discussed. It gives one more evidence that the ZZO model could provide a unified description for the novel elasticity of dsDNA and supports the conclusion that the base-stacking interaction plays an important role for the elasticity of dsDNA.