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Let $S$ be a 4-generated pseudo-symmetric semigroup generated by the positive integers $\{n_1, n_2, n_3, n_4\}$ where $\gcd(n_1, n_2, n_3, n_4) = 1$. $k$ being a field, let $k[S]$ be the corresponding semigroup ring and
$I_S$ be the defining ideal of $S$. $f_*$ being the homogeneous summand of $f$, tangent cone of $S$ is $k[S]/{I_S}_*$ where ${I_S}_* =< f_*|f \in I_S >$. We will show that the  "Hilbert function of the local ring (which is isomorphic to the tangent cone) for a 4 generated pseudo-symmetric numerical semigroup $<n_1,n_2,n_3,n_4>$ is always non-decreasing when $n_1<n_2<n_3<n_4$" by an explicit Hilbert function computation.