Frequency hopping spread spectrum is an effective technique used to mitigate the effects of narrowband interference. Traditional random frequency hopping (RFH), which can be categorized as a channel ignorant scheme, gives worse performance than channel-aware schemes such as matched frequency hopping, clipped matched frequency hopping and advanced frequency hopping, in frequency selective fading channels. However, these channel-aware schemes are more easily disrupted by adaptive jammers. In this paper, a modified RFH scheme is proposed that enhances the performance of RFH in frequency selective fading channels while also providing better protection against jamming.