The implementation of a machine learning algorithm for measuring refractive index of liquid samples using Fresnel reflection at the tip of a fiber is proposed in order to overcome the measurement ambiguity between samples having refractive index values below and above the effective refractive index of the fiber fundamental mode. This is the first time that a machine learning algorithm is implemented in a fiber refractometer. The algorithm, used for pattern classification, is the Support Vector Machine (SVM). The sensing head is formed by two-cascaded cavities that generate an interference pattern that changes each time the fiber is immersed in a different sample. The changes in the interference pattern are classified by the proposed algorithm, which extends the sensing range and eliminates any ambiguity in the obtained RI values. The proposed system is also self-referenced, and therefore it is unaffected by any intensity change of the optical source. A theoretical model and experimental results are presented in detail to demonstrate the effectiveness of the proposed system.