Symmetric regression deals with a reversible functional relationship between (Y, X) regardless of the direction of regression. Orthogonal, Geometric Mean, Pythagorean, Deming regression are valuable examples. However, contamination in the data can have a seriously adversarial effect on estimation. Therefore, a robust methodology for symmetric regression is proposed, that is built on the basics of Trimmed Least Squares: the reversible regression line is fitted on a subset of the data whereas potential outliers are discarded.