How does crossing over during meiosis lead to genetic variation?

Crossing over happens in prophase I when the homologous chromosomes are sy naps ed. The two inner chromoatids exchanges sections with each other. This means that after the exchange the inner two chromatids have new combinations of alleles than their parents had. The two outer chromatids still have the parental combinations.So there are more kinds of chromatids ready to go into the gametes than there were before. This is an increase in variation.