A methodology to design a multipoint fiber refractometer based on the Coherent Optical Frequency Domain Reflectometry (C-OFDR) technique is presented; in this refractometer, the nonlinearity effect generated by the scanning in optical frequency is reduced by a proper design of each sensing head; eliminating the need for the auxiliary interferometer commonly used for reducing this effect. Experimental demonstration on the nonlinearity effect in the sensing signal is presented. This effect is reduced by cutting the length of the processed signal in a cycle of scanning; to demonstrate this behavior, 100%, 50%, and 25% of the sensing signal from a scanning cycle are processed. However, it is not only about reducing the length of the sensing signal, but proper sensing head design also allows the reduced signal to be form by an integer number of cycles from each interference signal generated at the sensing heads, which in turns permit concatenation of the reduced signal without losing information. These three considerations, reduction of the signal in a scanning cycle, an integer number of cycles, and concatenation, generate stable and strong sensing signals. In this sense, the design of the sensing heads allows reducing the nonlinearity effect and possibility of a multipoint refractometer as well. Theoretical description and experimental results to demonstrate the effectiveness of the proposed method are presented. Design, construction, characterization and simultaneous implementation of three sensing heads are demonstrated.