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Contrary to the conventional wisdom that there is only one unique liquid state for any material, recent evidence suggests that there can be more than two liquid states even for a single-component substance. The transition between these liquid states is called a liquid-liquid phase transition. We report the detailed experimental investigation on the kinetics of the continuous spinodal-decomposition-type transformation of one liquid into another for triphenyl phosphite. From the analysis of the linear regime, we found that the correlation length, ξ, of fluctuations of the relevant order parameter diverges as ξ = ξ₀[(T_SD – T)/T_SD]^–ν (where ξ₀ = 60 nm and ν = 0.5) while approaching the spinodal temperature, T_SD. This is an indication of a critical-like anomaly associated with the liquid-liquid transition. We also revealed that the order parameter governing the liquid-liquid transition must be of a nonconserved nature.