  Narrowband spikes are observed in solar flares for several decades. However,
their exact origin is still discussed. To contribute to understanding of these
spikes, we analyze the narrowband spikes observed in the 800-2000 MHz range
during the impulsive phase of the November 7, 2013 flare. In the radio
spectrum, the spikes started with typical broadband clouds of spikes, and then
their distribution in frequencies changed into unique, very narrow bands having
non-integer frequency ratios. We successfully fitted frequencies of these
narrow spike bands by those, calculating dispersion branches and growth rates
of the Bernstein modes. For comparison, we also analyzed the model, where the
narrow bands of spikes are generated at the upper-hybrid frequencies. Using
both models, we estimated the plasma density and magnetic field in spike
sources. Then the models are discussed, and arguments in favor of the model
with the Bernstein modes are presented. Analyzing frequency profiles of this
spike event by the Fourier method, we found the power-law spectra with the
power-law indices varying in the -0.8 -- -2.75 interval. Because at some times
this power-law index was close to the Kolmogorov spectral index (-5/3), we
propose that the spikes are generated through the Bernstein modes in turbulent
plasma reconnection outflows or directly in the turbulent magnetic reconnection
of solar flares.
