Provided is a method for preparation of a composition comprising activated human CD8+ lymphocytes with phenotype of stem cell-like memory cells and natural killer (NK) lymphocytes. The method entails use of short-term activation of lymphocytes by CD3/CD28 activating agents followed by treatment with DNA-demethylating agent. The invention also provides a version of the method where addition of a CD3/CD28 activating agent is made a few days after initiation of CD4+ mediated activation of the CD8+ cells; this step is also disclosed as an improvement of related methods where autologous dendritic cells have been used to activate the lymphocytes. Also provided is a method for treatment of cancer using the cells obtained from the process.