In this note first we define the notion of {\it dual positive
implicative hyper $K$-ideal of type 4}, where for simplicity is
written by $DPIHKI-T4$. Then we give some related results.
Finally we determine all of hyper $K$-algebras of order 3,
 which have $D_{1}=\{1\}$, $D_{2}=\{1,2\}$ or $D_{3}=\{0,1\}$ 
as a  $DPIHKI-T4$.