The dielectric strength of the Debye relaxation in the binary mixtures of two isomeric monohydroxy alcohols, 2-ethyl-1-butanol (2E1B) and 4-methyl-2-pentanol (4M2P), is studied at low temperature near glass transition. Enhanced dielectric strength is exhibited in the mixtures, remarkably different from the mixing behaviors of the structural (alpha-) relaxation of generic liquids. A similar result is observed when analyzing the dielectric data of the binary mixtures of 2-ethyl-1-hexanol and 2-methyl-1-butanol reported in an early study. The unusual behavior of the dielectric strength in the mixtures reveals a new feature of the Debye relaxation in monohydroxy alcohols. Yet., the calorimetric measurements of the glass transition temperature in 2E1B-4M2P mixtures show a distinct negative deviation from the ideal mixing law. The explanation of the Debye relaxation is discussed with the results.