The present invention relates to novel disulfur bridge linkers containing hydrazine used for the specific conjugation of compounds/cytotoxic agents to a cell-binding molecule, through bridge linking a pair of thiols on the cell-binding molecule. The invention also relates to methods of making such linkers, and of using such linkers in making homogeneous conjugates, as well as of application of the conjugates in treatment of cancers, infections and autoimmune disorders.