With the emergent evolution in DNA sequencing technology, a massive amount of genomic data is produced every day, mainly DNA sequences, craving for more storage and bandwidth. Unfortunately, managing, analyzing and specifically storing these large amounts of data become a major scientific challenge for bioinformatics. Therefore, to overcome these challenges, compression has become necessary. In this paper, we describe a new reference-free DNA compressor abbreviated as DNAC-SBE. DNAC-SBE is a lossless hybrid compressor that consists of three phases. First, starting from the largest base (Bi), the positions of each Bi are replaced with ones and the positions of other bases that have smaller frequencies than Bi are replaced with zeros. Second, to encode the generated streams, we propose a new single-block encoding scheme (SEB) based on the exploitation of the position of neighboring bits within the block using two different techniques. Finally, the proposed algorithm dynamically assigns the shorter length code to each block. Results show that DNAC-SBE outperforms state-of-the-art compressors and proves its efficiency in terms of special conditions imposed on compressed data, storage space and data transfer rate regardless of the file format or the size of the data.