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The present invention provides a method for efficiently and constantly producing CD4/CD8 double-positive cells (that may further be induced into CD8 single-positive cells) comprising steps of (1) separating from a cell population containing hematopoietic progenitor cells, cells that express one or more molecules selected from a group consisting of CD24、CD62L、CD90、CD143、CD263、Notch3、CD32、CD39、CD49a、CD164、CD317、CD200、CD218a、CD7、CD144、CD56、CD226、CD262, and CD325, and/or cells that do not express one or more molecules selected from a group consisting of CD49f、CD51、CD102、CD42b、CD61、CD62P、CD69、CD102, and CD156c, and (2) differentiating the cells obtained in (1) to CD4/CD8 double-positive cells.