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In this correspondence paper, the wavelet transform, which is an important tool in signal and image processing, has been generalized by coalescing wavelet transform and fractional random transform. The new transform, i.e., fractional random wavelet transform (FrRnWT) inherits the excellent mathematical properties of wavelet transform and fractional random transform. Possible applications of the proposed transform are in biometrics, image compression, image transmission, transient signal processing, etc. In this correspondence paper, biometrics is chosen as the primary application; and hence, a new technique is proposed for securing fingerprints during communication and transmission over insecure channel.