In this paper we present a novel algorithm for the detection of dark linear structures, which appear in digital dermoscopy images of skin lesions and they are called as streaks in relevant literature. The proposed algorithm is capable of detecting such linear structures using local image curvature information obtained by the Hessian matrix. A linear structure is characterized as streak, based on its geometric characteristics. The streak detection algorithm is applied to a number of dermoscopy images containing malignant and non-malignant skin lesions. In this work we propose also a new class of streak based image features and we investigate their value in image classification according to malignancy.