  Let $R$ be a commutative Noetherian ring and $D$ be a discrete Hodge algebra
over $R$ of dimension $d>\text{dim}(R)$. Then we show that
  (i) the top Euler class group $E^d(D)$ of $D$ is trivial.
  (ii) if $d>\text{dim}(R)+1$, then $(d-1)$-st Euler class group $E^{d-1}(D)$
of $D$ is trivial.
