Orthogonal frequency division multiplexing (OFDM) is sensitive to frequency offset since it causes inter-carrier interference (ICI). Frequency offset results from the receiver's crystal oscillator inaccuracy, Doppler spread, or distortion. The pulse shaping function technique has proven its potential to combat ICI. To enhance the OFDM tolerance against the frequency offset, we introduce the improved double-jump 1 filter. The novel filter is then optimized given a representative system configuration. We finally demonstrate the effectiveness of the proposed filter in regard to the other novel pulses. This work serves to increase the wireless traffic demand.