The electronic structures and atomic magnetic moments of Nin clusters ( n = 2-6) have been studied. Compared with crystalline nickel, some clusters increase obviously in magnetism; some decrease obviously; and some show ferrimagnetism. The symmetry of clusters has great effect on magnetic moment. If they are similar in symmetry, the clusters are similar in magnetic moment. The magnetic moment for small clusters does not seem to increase or decrease monotonically with the change in their size, because adding or removing one atom may fully change the symmetry of small clusters. As the surface layer of ultrafine particles is made of many different polyhedrons with low symmetry and the alignment of the polyhedrons is complicated, the whole surface layer presents shortrange order. The calculated results explain the abnormal phenomena about surface magnetism that have been in existence for a long time.