Aims. The purpose of this work is to investigate a new frequency separation of stellar p-modes and its characteristics. Methods. Frequency separations are deduced from the asymptotic formula of stellar p-modes. Then, using the theoretical adiabatic frequencies of stellar model, we compute the frequency separations. Results. A new separation σ_l-1 l+1(n), which is similar to the scaled small separation d_l l+2(n)/(2l+3), is obtained from the asymptotic formula of stellar p-modes. The separations

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... σ_l-1 l+1(n) and d_l l+2(n)/(2l+3) have the same order. And like the small separation, σ_l-1 l+1(n) is mainly sensitive to the conditions in the stellar core. However, with the decrease of the central hydrogen abundance of stars, the σ_02 and σ_13 more and more deviate from the scaled small separation. This characteristic could be used to extract the information on the central hydrogen abundance of stars.