Code-based fringe projection profilometry (CBFPP) is widely applied to 3-D shape measurements due to its high accuracy and simple structure. However, phase-jump errors easily occur around the boundary of each period-wrapped phase, as the phase-jump regions are unstable. In this article, a preavoided method is proposed to suppress the phase-jump errors. The proposed method automatically generates an additional staggered fringe order by referring to the in-built fringe order, without the need of projecting further fringe patterns or altering the fringe sequence. Moreover, by employing a simple optimization algorithm, the proposed method is effective in eliminating the frequently occurring error propagation problem of current processing frameworks. The experimental results show that the proposed method is applicable for the correction of phase-jump errors for all types of code-based fringe projection profilometry methods under various scenarios.