This paper discusses the construction of rigid formation from arbitrary non-rigid components in two-dimensional space. Specifically, we focus on developing strategies for the construction sequences under the premise of building minimum number of links between the non-rigid components. Three operations, namely spindle splitting, rigid component shrink and edge floating, are proposed. The scenarios of acquiring a rigid formation from different kinds of non-rigid components are discussed respectively. It is proved that our strategy will guarantee the rigidity of the obtained formation with minimum number of inserted links, and will cover all the possible solutions during the construction process.