In the pursuit of bolstering user safety, social media platforms deploy active moderation strategies, including content removal and user suspension. These measures target users engaged in discussions marked by hate speech or toxicity, often linked to specific keywords or hashtags. Nonetheless, the increasing prevalence of toxicity indicates that certain users adeptly circumvent these measures. This study examines consistently toxic users on Twitter (rebranded as X) Rather than relying on traditional methods based on specific topics or hashtags, we employ a novel approach based on patterns of toxic tweets, yielding deeper insights into their behavior. We analyzed 38 million tweets from the timelines of 12,148 Twitter users and identified the top 1,457 users who consistently exhibit toxic behavior, relying on metrics like the Gini index and Toxicity score. By comparing their posting patterns to those of non-consistently toxic users, we have uncovered distinctive temporal patterns, including contiguous activity spans, inter-tweet intervals (referred to as 'Burstiness'), and churn analysis. These findings provide strong evidence for the existence of a unique tweeting pattern associated with toxic behavior on Twitter. Crucially, our methodology transcends Twitter and can be adapted to various social media platforms, facilitating the identification of consistently toxic users based on their posting behavior. This research contributes to ongoing efforts to combat online toxicity and offers insights for refining moderation strategies in the digital realm. We are committed to open research and will provide our code and data to the research community.