  Let $H$ be an ample line bundle on a non-singular projective surface $X$, and
$M(H)$ the coarse moduli scheme of rank-two $H$-semistable sheaves with fixed
Chern classes on $X$. We show that if $H$ changes and passes through walls to
get closer to $K_X$, then $M(H)$ undergoes natural flips with respect to
canonical divisors. When $X$ is minimal and its Kodaira dimension is positive,
this sequence of flips terminates in $M(H_X)$; $H_X$ is an ample line bundle
lying so closely to $K_X$ that the canonical divisor of $M(H_X)$ is nef. Remark
that so-called Thaddeus-type flips somewhat differ from flips with respect to
canonical divisors.
