In this work, we demonstrate a transferrable single crystalline 4H-SiC nanomembrane (SiC NM) released from a SiC-on-insulator (SiCOI) wafer. High resolution X-ray diffraction (XRD) and atomic force microscopy (AFM) were performed on the SiC NM and confirmed similarly good crystallinity and surface morphology. In addition, the refractive index and extinction coefficient of the SiC NM were investigated using ellipsometry analyses. Despite its thinness (i.e., 200 nm), the SiC NM achieved an absorption greater than 40% in the wavelength range of 200-260 nm with a maximum absorption of 73.8% at 256 nm. Our transferrable SiC NM provides not only good mechanical flexibility, but also exhibits excellent ultraviolet (UV) light absorption which could be readily utilized for high sensitivity flexible UV detectors.