A patient restraining device is secured to a patient supporting structure to more safely support a persons body during transport from one place to another. The device includes a sheet of fabric and connector straps secured to the fabric. After the device is fastened to the patient supporting structure, and the person is positioned on the patient supporting structure, the fabric is wrapped about the persons body, and the connector straps are secured about the fabric and the persons body. Among other things, the device may be used to increase the “patient capacity” of an otherwise conventional ambulance cot.