Normal integration is a key step in dense 3D reconstruction methods such as shape-from-shading and photometric stereo. However, normal integration cannot be guaranteed between spatially unconnected normal maps, which can ultimately cause a shape deformation in surface-from-normals (SfN). For the first time, this paper presents an efficient approach to address the fundamental problem of surface reconstruction from unconnected normal maps (denoted as "SfN+") using discrete geometry. We first design a normal piece pairing metric to measure the virtually pairing quality between two unconnected normal fragments, which is used as a new constraint for the boundary vertexes during mesh deformation. We then adopt a normal connecting significance indicator to adjust the influence of virtually connected vertexes, which further improves the overall shape deformation. Finally, we model the shape reconstruction of unconnected normal maps as a light-weight energy optimization framework by jointly considering the relaxation of connecting constraints and overall reconstruction error. Experiments show that the proposed SfN+ achieves a robust and efficient performance on dense 3D surface reconstruction.