Traffic light recognition is an indispensable elemental technology for automated driving in urban areas. In this study, we propose an algorithm that recognizes traffic lights and arrow lights by image processing using the digital map and precise vehicle pose which is estimated by a localization module. The use of a digital map allows the determination of a region-of-interest in an image to reduce the computational cost and false detection. In addition, this study develops an algorithm to recognize arrow lights using relative positions of traffic lights, and the arrow light is used as prior spatial information. This allows for the recognition of distant arrow lights that are difficult for humans to see clearly. Experiments were conducted to evaluate the recognition performance of the proposed method and to verify if it matches the performance required for automated driving. Quantitative evaluations indicate that the proposed method achieved 91.8% and 56.7% of the average f-value for traffic lights and arrow lights, respectively. It was confirmed that the arrow-light detection could recognize small arrow objects even if their size was smaller than 10 pixels. The verification experiments indicate that the performance of the proposed method meets the necessary requirements for smooth acceleration or deceleration at intersections in automated driving.