We define Lawrence-Krammer representation of the pure braid group Pn on band generators. For t= q−5/2 and q2 ̸= 1,, we prove that the complex specialization of Lawrence-Krammer representation P4 7→ GL6(Z[qپ}1]) is irreducible if and only if q ̸= e . A similar result for the pure braid groupP3 was done by Abdulrahim and Al-Tahan.