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Balanced Incomplete Block Designs (BIBD) are the designs obtained from the arrangement of symbols in blocks following established rules and satisfying relevant necessary conditions. BIBDs have broad applications in many fields.The entries in a Hadamard matrix H are all +1’s or -1’s, satisfying the property HHT = n In [2]. Rhotrix is a new concept in mathematics having applications in cryptography. In this paper, using SBIB designs the Hadamard Rhotrices are constructed. AMS Subject classification: 05B05, 05B20, 62K10.