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In this paper we calculate the squaring operations in the 4connective fibre spaces over the classifying spaces of the exceptional Lie groups. Let G be a compact, 1 -connected and simple Lie group. As is well known, its classifying space BG is 3-connected and H*(BG', Z) ~Z. Choose a generator y^H^(BG',Z). Then the 4-connective fibre space BG over BG is, by definition, the homotopy fibre of y^:BG— > K(Z,ty. Note that BG is a classifying space of G, the 3-connective fibre space over G. Here we quote the results in [2] and [4]. Define the sets Jl (/ = 2, 4, 6, 7, 8) as follows:

Squaring operations in the {4}-connective fibre spaces over the classifying spaces of the exceptional Lie groups