The proposed method for tumor screening ("Oncotest") is based on detecting substances (calcium-histone complexes) in the human blood which are markers of malignant neoplasia. Using "Oncotest" in a series of 5411 cases, we identified malignant tumors of various histogenesis (cancer, sarcoma) arising in different sites in 69 cases. "Oncotest" is especially important for early (pre-clinical) detection of malignant neoplasms during preventive population screenings.