Electroencephalographic (EEG) signals are constantly superimposed with biological artifacts. In particular, spontaneous blinks represent a recurrent event that cannot be easily avoided. The main goal of this paper is to present a new algorithm for blink correction (ABC) that is adaptive to inter- and intra-subject variability. The whole process of designing a Brain-Computer Interface (BCI)-based EEG experiment is highlighted. From sample size determination to classification, a mixture of the standardized low-resolution electromagnetic tomography (sLORETA) for source localization and time restriction, followed by Riemannian geometry classifiers is featured. Comparison between ABC and the commonly-used Independent Component Analysis (ICA) for blinks removal shows a net amelioration with ABC. With the same pipeline using uncorrected data as a reference, ABC improves classification by 5.38% in average, whereas ICA deteriorates by -2.67%. Furthermore, while ABC accurately reconstructs blink-free data from simulated data, ICA yields a potential difference up to 200% from the original blink-free signal and an increased variance of 30.42%. Finally, ABC's major advantages are ease of visualization and understanding, low computation load favoring simple real-time implementation, and lack of spatial filtering, which allows for more flexibility during the classification step.