The nature of modern data is increasingly real-time, making outlier detection crucial in any data-related field, such as finance for fraud detection and healthcare for monitoring patient vitals. Traditional outlier detection methods, such as the Local Outlier Factor (LOF) algorithm, struggle with real-time data due to the need for extensive recalculations with each new data point, limiting their application in real-time environments. While the Incremental LOF (ILOF) algorithm has been developed to tackle the challenges of online anomaly detection, it remains computationally expensive when processing large streams of data points, and its detection performance may degrade after a certain threshold of points have streamed in. In this paper, we propose a novel approach to enhance the efficiency of LOF algorithms for online anomaly detection, named the Efficient Incremental LOF (EILOF) algorithm. The EILOF algorithm only computes the LOF scores of new points without altering the LOF scores of existing data points. Although exact LOF scores have not yet been computed for the existing points in the new algorithm, datasets often contain noise, and minor deviations in LOF score calculations do not necessarily degrade detection performance. In fact, such deviations can sometimes enhance outlier detection. We systematically tested this approach on both simulated and real-world datasets, demonstrating that EILOF outperforms ILOF as the volume of streaming data increases across various scenarios. The EILOF algorithm not only significantly reduces computational costs, but also systematically improves detection accuracy when the number of additional points increases compared to the ILOF algorithm.