Thin form factor and placement-insensitivity are essential qualities of planar RFID antennas. Placement insensitivity can be achieved by introducing a conducting back plane. As the antennas become thinner, most of the energy is stored in the form of parallel plate modes resulting in the reduction of the bandwidth. Edge treatment in the form of serrations can be used to improve the bandwidth of such antennas. Researchers have investigated the use of serrations in resonant length antennas for bandwidth improvement. However, the behavior of serrations in non-resonant length antennas has not been studied in detail. This paper examines the changes in characteristic modes of non-resonant length antenna due to the change in the dimensions of serrations and proximity to the back plane. Statistical analysis is performed to ascertain the effect of antenna thickness, serration depth and serration width on the characteristic modes of the antenna.