Selective reflection of 852-nm laser radiation from the interface between cesium vapor and the sapphire window of a 30-micrometer-thick microcell was used to record an extreme increase in the probability of the F_g=3→F_e=5 transitions associated with the Cs-atom D_2 lines in magnetic fields with inductions ranging from 300 to 3200 Gauss. We showed that a group of seven transitions F_g=3, m_F=−3, −2, −1, 0, +1, +2, +3→F_e=5, m_F=−2, −1, 0, +1, +2, +3, +4 was formed in accordance with the selection rules Δm_F=+1 for σ^+-circularly-polarized radiation. These seven transitions have much higher probabilities in 500–1000 Gauss magnetic fields, with three of the transitions having probabilities higher than all of the other transitions originating from the level F_g=3. In magnetic fields with induction greater than 3000 Gauss, this group of seven transitions at the high-frequency end of the spectrum is completely separate from the group of transitions with F_g=3→F_e=4. Comparison of the frequencies and probabilities of these seven atomic transitions with those for the transitions F_g=3→F_e=5 showed good agreement between theory and experiment. We also discuss potential practical applications for these transitions.