The S = 1/2 Heisenberg antiferromagnet on the Lieb lattice accompanied by frustrating interactions is studied by the numerical-diagonalization method. Numerical results suggest that the model of the lattice obtained by combination of the Lieb lattice and the square lattice shows nontrivial states with nonzero spontaneous magnetization smaller than one third of the saturation magnetization when the strength of the frustrating interaction is in a specific region. In the region, the spontaneous

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... netization gradually changes by varying the strength of the frustration. We find that the quantum effect in frustrating interactions is related to the appearance of the phase in which such weak spontaneous magnetizations occur.