The choice of an appropriate method for fitting a straight line to data is one of the major procedural problems in bivariate allometric analysis. Commonly used techniques, such as ordinary least-squares regression and major axis, are derived from the general structural relationship model and thus require some knowledge about the distribution of the data. In this paper, we explore a nonparametric alternative, referred to as “rotation method”, which involves no assumptions about error distributions. It is symmetrical in the two variables and highly resistant against the influence of outlying data points. In this initial study, eight alternative versions of line-fitting by rotation are compared, using simulated data. The versions with the best overall performance are applied to empirical data from selected examples in biological anthropology. A comparison with conventional parametric methods reveals some marked advantages of the rotation method for descriptive allometric studies, indicating that further investigation into procedures of this kind is clearly warranted.