  In this paper we propose and prove an anticyclotomic Iwasawa main conjecture
for Heegner points on supersingular elliptic curves with $a_p=0$. The result
has a "$\pm$" nature in the sense of Kobayashi. The proof uses a recent work of
the second author on one divisibility in the Iwasawa--Greenberg main conjecture
for Rankin-Selberg $p$-adic $L$-functions, together with an argument of Howard
(adapted to our "$\pm$"-situation). As a byproduct, we also obtain an
improvement of Skinner's result on a converse to the Gross--Zagier--Kolyvagin
theorem.
