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Splitting a NURBS patch

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If I have for example 16x16 control-points for a NURBS patch (and a corresponding knot vector with uniformly increasing values), is it possible to split this patch into 4 9x9 patches, without changing the tesselated vertex output ? In my current setup, the data in the first column of a patch is the same as the data in the last column of the previous patch, but ofc the resulting tesselated vertex data does not match, as the patch doesnt directly pass the control-points. Is there any way to change this, which could be comprehendable for a 19 year old stundent with lacking maths education ? Or are the options I have basically limited to going back to bezier patches or making sure I get my nurbs patches in the size I''ll need in the end ?

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