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We consider the irreducibility of Generalised Laguerre Polynomials fornegative integral values given by$L_n^{(-1-n-s)}(x)=\displaystyle\sum_{j=0}^{n}\binom{n-j+s}{n-j}\frac{x^j}{j!}.$For different values of $s,$ this family gives polynomials which are of greatinterest. It was proved earlier that for $0 \leq s \leq 60,$ these polynomialsare irreducible over $\mathbb{Q}.$ In this paper we improve this result upto $s\leq 88.$

Extension of Irreducibility results on Generalised Laguerre Polynomials $L_n^{(-1-n-s)}(x)$