The current gold standard of malaria diagnosis is the manual, microscopy-based analysis of Giemsa-stained blood smears, which is a time-consuming process requiring skilled technicians. This paper presents an algorithm that identifies and counts red blood cells (RBCs) as well as stained parasites in order to perform a parasitaemia calculation. Morphological operations and histogram-based thresholding are used to extract the red blood cells. Boundary curvature calculations and Delaunay triangulation are used to split clumped red blood cells. The stained parasites are classified using a Bayesian classifier with their RGB pixel values as features. The results show 98.5% sensitivity and 97.2% specificity for detecting infected red blood cells.