How to derive normals for newly created vertices?

Hi, let's say I have an edge, which is shared by 2 faces.
Now I split the edge into two parts (i.e. I introduce a new vertex somewhere along the edge). And the introduction of this new vertex also split up the face into two parts.

Now the normal for the newly created vertex will be re-calculated (by taking the average of the faces that it belongs to).

But I want the normal to be derived from the original edge.

Is there any script that does this?

To give you a better picture, when I split an object into 2, then the two parts will have overlapping vertices whereever it got split.
I want it to have the same normal as the original object.
Since the original object did not have a vertex there, the normal will have to be derived.