B-spline basis is widely used in construction of curves and surfaces for its excellent property of being totally positive and locally adjustable. Uniform B-spline as a special case of B-spline is also worth researching for its convenience in operation in industry modeling. In 2003, Delgado and Pe?a had given another new form of curve, which is constructed by a new totally positive basis (DP-NTP basis). This kind of curve shows obvious advantage in computing, for the reason that it has linear complexity. Meanwhile, it has good shape preserving property. But regretfully it is not locally adjustable as how B-spline curves do. As to achieve the advantages of both, and as well make exchanging and transferring data possible between various systems, the conversion between uniform B-spline curves and DP-NTP curves is presented. Examples show that this result can be widely used in efficient evaluation of locally adjustable curves and surfaces.