Merge Face Without Creating NGon

Hello,

I’m trying to use the _mergefaces command (or edge deletion) to simplify a mesh in a specific but simple manner, and am wondering if there is a way to avoid generating an Ngon. As an example, imagine a simple plane divided into 4 quads. I want to convert this plane into two longer quads instead of four. By using merge edge on two of the edges (or selecting the edges and deleting them), I end up creating two 6-sided N-Gons instead of 2 quads because the vertex in the middle of the remaining three long edges is not removed. Here is an illustration:

I was wondering if any one has a simple way of executing similar edge removal without generating NGons. I feel like there is some simple command to do this, or remove the extra vertices, that I’m overlooking. Right now if I want to perform similar simplifications I’m either re-drawing the faces or do some other convluted thing to get rid of the extra faces.

Note that I’m actually dealing with more complicated and larger meshes than simple planes - this is just a good example demonstrating the issue.

Thank you