In the single cross over there is only one chiasma. In other words there is only one point of contact between the homologous chromosomes. In double cross over, contact between homologous chromosomes is established at two points.
Recombination will be more in double cross over than in a single cross over as more quantity of genome is exchanged between homologous chromosomes. Depending on the number of strands involved, double cross over has been classified into the following categories.
(a) Two strand cross over:
In this type of double cross over, the same (two) non sister chromatids are involved in the cross over at both the points. As a result, two chromatids are cross over chromatids and the other two non cross over chromatids.
(b) Three strand cross over:
In this case, one of the points of contact is between the two chromatids while the second contact is between one of the chromatids of first contact and another non sister chromatid. In this way three chromalids are involved in cross over, while only one will be a non cross over chromatid.
(c) Four strand cross over:
In this type of cross over, all the four chromatids are involved in the cross over. First chiasma involves two chromatids, while the second chiasma involves the other two chromatids of the tetrad with the result there is no non cross over chromatid. Such chiasmata are called complementary chiasmata.