We show a natural form of the interaction between unparticle and supersymmetry. Using the couplings of unparticle to supersymmetry presented, as examples, we calculate the differential decay rates for the processes ${\it {\tilde f}}\to {\it f}+{\cal U}_{3/2}$, ${\it {\tilde ��}}^0\to{\it ��}+{\cal U}_{3/2}$, ${\it {\tilde ��}}^\pm\to W^\pm+{\cal U}_{3/2}$ and ${\it {\tilde ��}}^0\to Z^0+{\cal U}_{3/2}$. Finally, we discuss the phenomenological implication of our results and give some comments.

Version published in Physical Review D