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A detailed analysis is made of the effect of reflection of low-energy secondary emitted electrons on the susceptibility diagrams for multipactor breakdown between two parallel metal plates. The problem is studied using both analytical and numerical methods. The left boundary of the first resonance zone for the multipactor is shown to be significantly modified when electrons with impact energy of the order of their initial energy are completely reflected. Specifically, in this case, the multipactor avalanche may grow even when the gap between the metal plates is very narrow if the applied RF voltage is high enough to provide electron acceleration up to energies exceeding the first crossover energy of the secondary emission curve. This effect is proposed as a means for experimentally investigating the reflection properties of low-energy electrons from the surface of different materials.