To construct a perpendicular line that is not a perpendicular bisector using the folding paper method, the statement that best describes a step in this construction is:
"Fold the paper so that the endpoint matches up with the other endpoint."
This step involves folding the paper such that one endpoint of the segment aligns with the other endpoint, creating a crease that will define a line that is perpendicular to the original segment at a point other than the midpoint.