A method and blood bag, whereby a substantial volume of concentrated whole blood can be quickly and easily recovered from the cardiopulmonary bypass (CPB) circuit of a patient immediately following cardiac or thoracic vascular surgery. This is achieved in an operating room, by transferring most of the blood in the CPB circuit into a sterile bag located in the surgical field, removing the bag with blood from the surgical field, and outside the surgical field, but preferably in the operating room, hemo-concentrating the blood in the bag, while the bag is fluidly connected to the bypass system hardware. A novel blood bag (or hemo-bag) system is especially adapted for use with the method of the present invention. The new hemo-bag system comprises a closed, sterile bag of substantially transparent, bio-compatible material, defining upper and lower ends. An infusion port is located at the upper end of the bag. An outlet port, an inlet port, and an IV line are situated at the lower end of the bag. A baffle is preferably located inside the bag, for directing upward flow entering the bag through the inlet port, away from the outlet port. Each of the ports and line terminate in connector structure, and can be opened or closed by way of conventional clips and caps.