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The paper deals with a square composite saddle-shaped cable roof 30 × 30 m in the plan, which is formed by two orthogonal cable groups joined with a compliant support contour. The kinematic invariability of the roof is achieved by prestressing the cable net. From the viewpoint of material consumption, the cable roof has rational geometrical characteristics. A hybrid composite cable on the basis of CFRP, GFRP, and steel is considered as a material for contour cables. The load-carrying and the stabilizing cables are made of steel. Prestress losses in the stabilizing cables are determined for three variants of prestressing. The possibility of reducing the consumption of cable materials by prestressing each cable of the net by an individual force is revealed.