In comparison with the conventional grain-oriented electrical steels (the so-called CGO steels), the high permeability electrical steels (the so-called Hi-B steels) including those of nitrided steels possess higher magnetic properties, but their processing window is narrow. In particular, a near brass--oriented texture which rotated around the normal direction of sheets from Goss orientation is often observed in improperly processed sheets of Hi-B steels, i.e, this type of sheet possesses a correct morphological structure of well abnormally grown grains, but a poor crystallographic texture with low magnetic properties. The underlying mechanism is less dealt with in literature in comparison with the formation of Goss texture. Thus, the objective of this work is to analyze the formation mechanism of this texture component. For this purpose, XRD and EBSD technique were applied to reveal both macro- and micro-textures from the shear texture of hot rolled plate surface to primarily and secondarily annealed sheets paying particular attention to the origin and relationship of Brass-oriented grains with their surrounding grains. It is demonstrated that Brass-oriented grains are formed by the rotation of Goss-oriented grains around the normal direction in the sheared surface layer of hot rolled plate when the shearing around transverse direction is restrained. Compared with the close relation between Goss and {111}<112> oriented grains, similar behaviors during cold rolling and annealing occur between brass-- and {111}<110>-oriented grains, namely, the latter are also inclined to be adjacently related and mutual transformation could occur between those deformation grains and recrystallization grains. In particular, a higher rolling reduction reduces Goss grain number much significantly, whereas it favors the retention of brass- and {111}<110>-oriented grains leading to preferred growth of brass-oriented grains. In the condition of easy growth of Brass grains with their {110} being parallel to rolling plane like Goss grains in the thinner sheets, the much fewer Goss grains could not swallow the brass-oriented grains. Thus, this technical issue of producing grain oriented electrical steels with high magnetic properties can be understood in terms of fundamentals of texture evolution during deformation and recrystallization of bcc metals.