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Let d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(x)d(y), d(xy) = d(y)d(x) on L. With this, a theorem of Ali et al. [14] can be deduced.