I 'm trying to add an edge in the corner. As I link the two vertices together, here what happens:
How can I prevent this distortion?
You’ve already added an outside loop no need for adding an extra one. To merge two vertices either selecting everything with ‘A’ or 'A’x2 then pressing W -> ‘Remove doubles’ or selecting those individual vertices and pressing ‘Alt+M’ -> ‘Merge to Center’.
To make sharper corners, either use the edge crease or add supporting edges like this…
There are some other details that I left out here that are used in more complex situations, but I try to avoid diagonals at the corners in many cases as they will create distortion. I am just assuming that this is what you were wishing to do by linking the verticies.
So sorry, I’ve misread your question. You can either use a knife tool ‘K’ or you could ad a vertex on and edge by selecting it subdividing it with ‘W’ --> Subdivide,then select both vertices that you want to connect and press J.
I saw a tute a long time ago to do this with minimal geometry changes (or at least, to keep the polygon count down). Let me try and find it, if I can’t, I’ll do it myself. It involves creating a complex loop inside the edges, and maintains all quads. It may take a day or so, though (I have to sleep now)