  We study the unzipping of double stranded DNA (dsDNA) by applying a pulling
force at a fraction $s$ $(0 \le s \le 1)$ from the anchored end. From exact
analytical and numerical results, the complete phase diagram is presented. The
phase diagram shows a strong ensemble dependence for various values of $s$. In
addition, we show the existence of an ``eye'' phase and a triple point.
