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
$\kappa(X)\geq 1$, 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.