A new analytical solution for the cumulative batch grinding equation for first-order breakage has been proposed. Knowledge of two basic parameters of attrition, the selection and breakage functions, is sufficient to solve the equation. The conservation equation of the weight fraction for different size intervals has been discretised with the maximum size as the last grid. This mode of dividing size is unlike the other methods commonly used. The advantage of this method is that not only does it involve no iterative technique but it does not rely on any approximation either. Moreover, it is computationally extremely simple and straightforward.