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This paper presents an improved scheme for the state-of-health (SOH) estimation, applicable to battery management system (BMS) of electric vehicles. The original scheme requires the prior information for the estimation, which is the prior SOH identified from the last charging. This limit implies that if a battery or its BMS is replaced, the prior SOH stored within the BMS no longer matches with the actual SOH, resulting in a critical error. To avoid this potential but critical pitfall, we newly devise an improved SOH estimation scheme. The original scheme is revised by adopting the fixed-point iteration method into its parameter estimation. By removing dependencies on the prior information, the revised scheme can function regardless of such replacements. The revised scheme is experimentally validated and demonstrated that even without the prior information, it can satisfy the requirement of the SOH estimation (within 3%) thanks to its improved design. [ABSTRACT FROM AUTHOR]