Quantum error-correcting codes protect quantum information against undesirable noise in quantum computation and quantum communication. It is one of important problems that constructing very good quantum codes. There are two methods that use binary codes to construct quantum codes,one is CSS construction, another is Steane construction. These two methods are all based on the construction of binary self-orthogonal codes. Combinational construction of binary self-orthogonal codes is investigated in this paper. From known codes chains of binary self-orthogonal codes and their dual codes chains with given dual distance, new binary self-orthogonal codes of dual distance three, four, five and six are constructed. Based on these results, for each satisfying , S-chains with parameters and are constructed. According to Steane's construction, many very good quantum codes of distance five and six are constructed by the obtained S-chains, some of these quantum codes are new and some of these quantum codes have improved parameters than previously known codes.