Fractional Interference Alignment (FIA) is a transmission scheme which achieves any value between [0,1] for the Symbols transmitted per Antenna per Channel use (SpAC). FIA was designed in [1] specifically for Finite Alphabet (FA) signals, under the constraint that the Minimum Distance (MD) detector is used at all the receivers. Similar to classical interference alignment, the FIA precoder also needs perfect channel state information at all the transmitters (CSIT). In this work, a novel Blind Fractional Interference Alignment (B-FIA) scheme is introduced, where the basic assumption is that CSIT is not available. We consider two popular channel models, namely: Broadcast channel, and Interference channel. For these two channel models, the maximum achievable value of SpAC satisfying the constraints of the MD detector is obtained, but with no CSIT, and also a precoder design is provided to obtain any value of SpAC in the achievable range. Further, the precoder structure provided has one distinct advantage: interference channel state information at the receiver (I-CSIR) is not needed, when all the transmitters and receivers are equipped with one antenna each. When two or more antennas are used at both ends, I-CSIR must be available to obtain the maximum achievable value of SpAC. The receiver designs for both the Minimum Distance and the Maximum Likelihood (ML) decoders are discussed, where the interference statistics is estimated from the received signal samples. Simulation results of the B-FIA show that the ML decoder with estimated statistics achieves a significantly better error rate performance when compared to the MD decoder with known statistics, since the MD decoder assumes the interference plus noise term as colored Gaussian noise.