This paper contains the detailed analysis of the following two-parameter family of piecewise smooth unimodal maps with one break point:
where and are real parameters varying in the range and . Primarily, the 2D bifurcation diagram in the -parameter plane is investigated. Particular attention is paid to the border-collision on bifurcation of the superstable -cycle of the map . The use of the symbolic representation of the superstable cycles is an interesting method to describe the structure of the periodicity regions of the 2D bifurcation diagram.