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The High Luminosity LHC requires dipole orbit correctors grouped in double aperture magnet assemblies. They provide a field of 3.1 T at 100 A in an aperture of 70 mm. The current standard design is a classical cosine-theta layout made with ribbon cable. However, the electric insulation of this cable is not radiation-resistant enough to withstand the radiation load expected in the coming years of LHC operation. A new design, based on a cable with polyimide insulator, that can replace the existing orbit correctors, is needed. The challenge is to design a magnet that fits directly into the existing positions and that can operate with the same busbars, passive quench protection, and power supplies. The new orbit corrector design meets high requirements on the field quality while keeping within the same mechanical volume and maximum excitation current. A collaboration of Swedish universities and Swedish industry has been formed for the development and production of a prototype magnet following a concurrent engineering methodology to reduce the time needed to produce a CCT magnet. The magnet has a 1 m long CCT dipole layout consisting of two coils. The superconductor is a commercially available 0.33 mm wire with polyimide insulation in a 6-around-1 cable. The channels in the coil formers, that determine the CCT layout, allow for 2 x 5 cable layers. A total of 70 windings makes that the coil current can be kept below 100 A. We will present the detailed design and preliminary quench simulations.