In this Letter, we explore another novel Ehrenfest scheme which can also be utilized in the P -V criticality research of RN-AdS black holes. The novel form of Ehrenfest scheme is neither the one in classical thermodynamics nor the analogy one proposed for grand-canonical ensemble in literatures. After a detailed derivation of the novel Ehrenfest equations, an analytical check is carried out at the critical point of P -V criticality of RN-AdS black holes. It is shown once again that the phase

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... nsition at the critical point is a second order one. Both the novel Ehrenfest scheme developed in this Letter and the classical Ehrenfest equations utilized in our former research can be applied to investigate the nature of phase transition at the critical point of P -V criticality of AdS black holes.