Cardiac magnetic resonance (CMR) imaging is an important technique for cardiac diagnosis. Measuring the scar in myocardium is important to cardiologists to assess the viability of the heart. Delayed enhancement (DE) images are acquired after about 10 minutes following injecting the patient with contrast agent so the infracted region appears brighter than its surroundings. A common method to segment the infarction from DE images is based on intensity Thresholding. This technique performed poorly for detecting small infarcts in noisy images. In this work we aim to identify the best threshold value to segment the infarction in case of segmentation using simple Threshold and propose a modified technique to improve the segmentation in noisy images. Our proposed technique is based on enhancing Thresholding using k-means clustering. We test our proposed model using computer simulated and real images with different contrast-to-noise ratio (CNR). We used F-score, which is a combined measure of the precision and sensitivity, to determine the performance of the proposed technique versus simple Thresholding. The results show that the proposed technique outperforms existing methods.