Although large language models (LLMs) have demonstrated impressive performance across a wide range of tasks, they remain prone to errors. A critical and highly sought-after capability is their ability to self-correct. While prior research has often depended on external tools or large proprietary models, this work explores self-correction in small language models (SLMs) through iterative fine-tuning using exclusively self-generated data. We propose the Self-Taught Self-Correction (STaSC) algorithm and its generalized variant, G-STaSC. Experimental results on a question-answering task highlight the effectiveness of STaSC over alternative methods and G-STaSC variations, offering significant insights into the mechanisms of self-correction. To facilitate further research, we provide open access to our user-friendly codebase and lightweight models.