Please ignore the prior post.
Let the remaining matchsticks be located at these coordinates on the xy-axes:
(0, 0) to (0, 1)
(0, 1) to (0, 2)
(0, 2) to (0, 3)
(2, 0) to (2, 1)
(2, 1) to (2, 2)
(2, 2) to (2, 3)
(3, 1) to (3, 2)
(3, 2) to (3, 3)
(0, 0) to (1, 0)
(1, 0) to (2, 0)
(0, 1) to (1, 1)
(1, 1) to (2, 1)
(2, 1) to (3, 1)
(0, 2) to (1, 2)
(1, 2) to (2, 2)
(2, 2) to (3, 2)
(0, 3) to (1, 3)
(1, 3) to (2, 3)