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 $sigma_{l-1 l+1}(n)$, 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 $sigma_{l-1 l+1}(n)$ and $d_{l l+2}(n)/(2l+3)$ have the same order. And like the small separation, $sigma_{l-1 l+1}(n)$ is mainly sensitive to the conditions in the stellar core. However, with the decrease of the central hydrogen abundance of stars, the $sigma_{02}$ and $sigma_{13}$ 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.
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