In this paper, a novel FM-chaos based noncoherent modulation technique is proposed. In this proposed Frequency-Modulated High Efficiency Differential Chaos Shift Keying (FM-HE-DCSK) with selective Orthogonalization scheme, superior qualities of HE-DCSK, like high data rate and bandwidth efficiency are preserved. The proposed scheme is also observed to provide improved BER performance, comparable to QCSK (Quadrature Chaos Shift Keying) and FM-QCSK, at lesser system complexity. A theoretical treatment on FM-chaos is developed to analyze the scheme and corresponding theoretical performance analysis is provided. Finally, it is shown that the proposed scheme outperforms UWB FM-DCSK in indoor UWB environment.