The five linear primary and secondary alcohols, n-propanol, isopropanol, n-butanol, 2-butanol and 2-pentanol, have similar chain lengths and a little different structures and they are measured by dielectric spectroscopy in this paper to investigate the properties of monohydroxy alcohols. It is found that the dielectric spectra of isopropanol and n-butanol show an abnormal variation. i.e., the relaxation peaks with the highest strength gradually increases with rising temperature in the range of about 145 K-175 K. The analyses state that the abnormal variation originated from that of the Debye dielectric relaxation strength (DDRS) in the monohydroxy alcohols at above temperatures. According to the theoretical model of the DDRS for the monohydroxy alcohols, the abnormal variation is considered as the results of the combined action of decrease and increase of the DDRS due to temperature and the transformation of the structure of the hydrogen bonding molecular chain caused by the alteration of the mobility of molecules, respectively. By comparing the relaxation time of the five monohydroxy alcohols, it is found that the conditions should be harsher to induce the above abnormal variation. In addition, the results also show that strength parameter of Debye processes, intrinsic vibration frequency of the relaxation units and their activation energy in the high-temperature limit in secondary alcohols also raises with the increasing number of carbon atoms, similar to that in the case of primary alcohols. These results could not only provide a new breakthrough point for the investigation of exotic properties in monohydroxy alcohols but also give a reference to explore the effect of molecular chain length on their dynamics.