Outlier detection is an important data mining technique. In this article, the triangle inequality of distances is leveraged to design a pre-cutoff value (PCV) algorithm that calculates the outlier degree pre-threshold without additional distance computations. This algorithm is suitable for accelerating various metric space outlier detection algorithms. Experimental results on multiple real datasets demonstrate that the PCV algorithm reduces the runtime and number of distance computations for the iORCA algorithm by 14.59% and 15.73%, respectively. Even compared to the new high-performance algorithm ADPOD, the PCV algorithm achieves 1.41% and 0.45% reductions. Notably, the non-outlier exclusion for the first data block in the dataset is significantly improved, with an exclusion rate of up to 36.5%, leading to a 23.54% reduction in detection time for that data block. While demonstrating excellent results, the PCV algorithm maintains the data type generality of metric space algorithms.