Abstract: In India, magic squares seem to have been known for more than two millennia. However, among the extant texts, a systematic introduction to the principles governing their construction can be found only in the work of Nārāyaṇa Paṇḍita (c. 1356 CE). He has dedicated one full chapter of his Gaṇitakaumudī to describe Bhadragaṇita, namely, methods for constructing magic squares of different orders. The focus of this talk would be to present the algorithm propounded by Nārāyaṇa Paṇḍita for constructing pan-diagonal magic squares of order 4 using only turagagati or horse-moves. Earlier studies by a few scholars starting with Datta and Singh have discussed this algorithm, showing how consecutive pairs get placed in horse-moves. Whereas, in our presentation, we shall demonstrate that the construction of the entire square can be made by employing only horse-moves. We shall also touch upon the properties exhibited by such pan-diagonal squares.