Log-based anomaly detection is an important task in ensuring the stability and reliability of software systems. One of the key problems in this task is the lack of labeled logs. Existing works usually leverage large-scale labeled logs from mature systems to train an anomaly detection model of a target system based on the idea of transfer learning. However, these works still require a certain number of labeled logs from the target system. In this paper, we take a step forward and study a valuable yet underexplored setting: zero-label cross-system log-based anomaly detection, that is, no labeled logs are available in the target system. Specifically, we propose ZeroLog, a system-agnostic representation meta-learning method that enables cross-system log-based anomaly detection under zero-label conditions. To achieve this, we leverage unsupervised domain adaptation to perform adversarial training between the source and target domains, aiming to learn system-agnostic general feature representations. By employing meta-learning, the learned representations are further generalized to the target system without any target labels. Experimental results on three public log datasets from different systems show that ZeroLog reaches over 80% F1-score without labels, comparable to state-of-the-art cross-system methods trained with labeled logs, and outperforms existing methods under zero-label conditions.