Non-destructive inspection of composite materials is a critical process in industries such as aerospace and construction, where structural integrity must be verified to prevent catastrophic failures. Ultrasonic testing is a widely used NDI method for detecting defects in composite parts, but its effectiveness depends on maintaining a water column between the probe and the part surface. Traditional automated coverage path planning (CPP) approaches fail to ensure full coverage, particularly along the edges of complex geometries where the loss of the water column can compromise inspection reliability. This paper presents a novel CPP method for robotic NDI that enhances inspection coverage by fitting the edges with parametric Bézier curves to ensure inspection around the edges before constructing the remainder of the path. The method then refines the path using a modified potential field algorithm and a redundant coverage elimination algorithm. The result of the proposed method is a largely automated, efficient NDI process while maintaining a high quality of inspection.