Relative position embedding (RPE) is a successful method to explicitly and efficaciously encode position information into Transformer models. In this paper, we investigate the potential problems in Shaw-RPE and XL-RPE, which are the most representative and prevalent RPEs, and propose two novel RPEs called Low-level Fine-grained High-level Coarse-grained (LFHC) RPE and Gaussian Cumulative Distribution Function (GCDF) RPE. LFHC-RPE is an improvement of Shaw-RPE, which enhances the perception ability at medium and long relative positions. GCDF-RPE utilizes the excellent properties of the Gaussian function to amend the prior encoding mechanism in XL-RPE. Experimental results on nine authoritative datasets demonstrate the effectiveness of our methods empirically. Furthermore, GCDF-RPE achieves the best overall performance among five different RPEs.