Create Quarter sections lines

[CCWeedcontrol]

I have polylines of the sections and monuments. I need to create quarter sections lines. I am not sure what is the best way to achieve this without connecting the lines manual. I am sure some one has come across this before. So if anyone can help me out that would be awesome. Pic 1 show what i have and pic.2 is what i am trying to achieve.

[HeatherBerg1]

You can download Quarter Quarter section lines for each state here: http://nationalcad.org/download/PLSS-CadNSDI-Data-Set-Availability.pdf. You would then want to look for the seconddivison layer within the geodatabase.