Absolutely. There are several methods but to me, the most secure is to sew the new line to the old with heavy thread (dental floss works fine)keeping them butted one end to the other end with loops - through one end then through the other then back, etc. Six or eight of those should suffice. Then, wrap the junction completely starting 3-4" above the junction to 3-4" below with electrical tape being careful not to make the wrap too thick. A safety tip; heat seal the ends to prevent the threads from pulling through the weave. When you pull it through, be careful at the sheaves.