Brief bursts of high-frequency (HF) and very high frequency (VHF) radio emissions unaccompanied by strong low-frequency radiation have been observed during initiation and propagation of lightning or thunderstorm electrical breakdown without leading to fully fledged lightning. This paper investigates a physical mechanism to generate such radio bursts by electrical discharge activity inside a thundercloud. When a discharge consists of many high-frequency emission sources, such as streamers, that generate currents in random directions, its radiation spectrum peaks in the HF and VHF bands, and the spectral magnitudes in low frequencies are much smaller or even negligible. Combined with recent observational findings, the present study suggests that lightning initiation may begin with a short burst of many randomly occurring small-scale discharges in a localized thundercloud region. Plain Language Summary How exactly lightning forms from electrical breakdown activity inside thunderclouds remains unclear. To answer this question, radio frequency (RF) radiation originating from thunderstorms is routinely measured and analyzed to investigate lightning dynamics. Recent multichannel radio observations clearly indicate that brief bursts of high-frequency RF radiation unaccompanied by lower-frequency waves can be generated during lightning formation. Such radio bursts have different spectral properties than well-documented RF radiation from lightning. This paper investigates a way for electrical breakdown activity to generate such radio bursts. We find those radio bursts can be generated by an electrical discharge consisting of a large number of elements that propagate in random directions. Our finding suggests that lightning may begin with many randomly occurring small-scale electrical discharges in a localized thundercloud volume. Recent multiband radio observations have also shown that bursts of HF and VHF radiation with only weak or even no accompanying sferic pulses (i.e., weak lower-frequency radiation) can be generated during thunderstorms. Examples of such RF bursts include the microsecond-long radiation from the initial breakdown of precursor events reported by Rison et al. (2016), which are thundercloud discharges not leading to fully fledged lightning, and narrow (e.g., ≤0.5 μs) VHF pulses that are the initiating events of a large fraction of lightning (Lyu et al., 2019; Marshall et al., 2019) and that also occur during lightning formation RESEARCH LETTER