Training of deep neural networks (DNN) in mission-critical scenarios involves increasingly more resources, which stimulates model stealing from prediction API at the cloud and violates the intellectual property rights of the model owners. To trace public illegal model copies, DNN model fingerprint provides a promising copyright verification option for model owners who want to preserve the model integrity. However, existing fingerprinting schemes are mainly based on output-level traces (e.g., mis-prediction behavior on special inputs) to cause limited stealthiness during model fingerprint verification. This study proposes a novel task-agnostic fingerprinting scheme based on saliency map traces of model prediction. The proposed scheme puts forward a constrained manipulation objective of saliency maps to construct clean-label and natural fingerprint samples, thus significantly improving the stealthiness of model fingerprints. According to extensive evaluation results on three typical tasks, this scheme is proven to substantially enhance the fingerprint effectiveness of existing schemes and remain highly stealthy of model fingerprints.