The so-called "λ/2-Zeeman technique" (HLZT) for studies of individual optical transition between Zeeman sublevels of atomic hyperfine structure in an external magnetic field of B = 10 - 2500 G is presented. Particularly, implementation of HLZT allows one to realize a direct determination of frequency shift and a strong modification of an optical transition probability between Zeeman components in a B-field. The main advantages of the method compared to "λ-Zeeman technique" (LZT) is that it allows one to study weak transitions. Particularly, with the help of fluorescence on 87Rb, D2 line, Fg = 1 → Fe = 3 transitions, three "forbidden" transitions in magnetic field B are detected and studied. Also, on 87Rb D1 line, Fg = 1, mF = 0 → Fe = 1, mF = 0 "forbidden" transition is detected when B ~ 400 G. A strong modification of the probability for these "forbidden" transitions is revealed. The theoretical model well describes the observed results.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.