Using a virtual probe method in molecular dynamics approach, we have explored the growing process of atomic clusters by adding atoms in a one-by-one manner to a tetrahedron up to 50 atoms and found that the growing path repeats a process of split-then-merge chaining. The sequential chains merge in the vicinity of the ones with atoms of magic number and then diverge, meaning that, in the cluster growing sequences, the merging of growing paths near magic clusters may increase the appearing probability of the most stable magic clusters. Findings not only demonstrate the possible ways of magic cluster growth but also further clarify the stability of such magic clusters.