  A mechanism of $1/f$ noise due to traps formed by impurities which have no
neighbors with close energies in their vicinity is studied. Such traps slowly
exchange electrons with the rest of conducting media. The concentration of
traps and proportional to it $1/f$ noise exponentially grow with decreasing
temperature in the variable range hopping regime. This theory provides smooth
transition to the nearest neighbor hopping case where it predicts a very weak
temperature dependence.
