Soap composition in the transparent solid cake (bar) form, having an improved hardness and an improved resistance to exudation (sweating). The composition contains, expressed by weight with respect to the total weight of the composition: a) from 25 to 40 % of a soap consisting of a salt of C10-C20 fatty acids or of their mixtures; b) from 2 to 50 % of isoprene glycol; c) from 0 to 48 % of a transparency agent, other than isoprene glycol, the total concentration of isoprene glycol and of transparency agent being between 25 and 50 %; and d) water in an amount less than or equal to 25 %. Application to the formation of bars of soap.