 Recombination change in two-locus haplotype frequencies

Let the four haplotype frequencies sum to one and define $D=x_{AB}{x}_{ab}-x_{Ab}{x}_{aB}=x_{AB}-p_A{p}_B$. Recombination at rate $r$ removes the excess association: $\Delta x_{AB}=\Delta x_{ab}=-rD$ and $\Delta x_{Ab}=\Delta x_{aB}=rD$. Marginal allele frequencies are unchanged. Hence $D<0$ generates more $AB$, whereas $D>0$ removes it; a claim that recombination always increases this combination is false.