  We construct a one parameter family of finite time blow ups to the
co-rotational wave maps problem from $S^2\times \RR$ to $S^2,$ parameterized by
$\nu\in(1/2,1].$ The longitudinal function $u(t,\alpha)$ which is the main
object of study will be obtained as a perturbation of a rescaled harmonic map
of rotation index one from $\RR^2$ to $S^2.$ The domain of this harmonic map is
identified with a neighborhood of the north pole in the domain $S^2$ via the
exponential coordinates $(\alpha,\theta).$ In these coordinates
$u(t,\alpha)=Q(\lambda(t)\alpha)+\mathcal{R}(t,\alpha),$ where
$Q(r)=2\arctan{r},$ is the standard co-rotational harmonic map to the sphere,
$\lambda(t)=t^{-1-\nu},$ and $\mathcal{R}(t,\alpha)$ is the error with local
energy going to zero as $t\rightarrow 0.$ Blow up will occur at
$(t,\alpha)=(0,0)$ due to energy concentration, and up to this point the
solution will have regularity $H^{1+\nu-}.$
