In a majority of the cases, error propagation studies in nuclear science and engineering use the sandwich formula, which is strictly applicable when the probability density function of the random input quantities (e.g., the basic cross-section data) are determined completely by the mean and covariances. The use of the sandwich formula, which is also referred to in the literature as traditional first-order sensitivity analysis or adjoint-based sensitivity and uncertainty analysis, requires the assumption of linearity assumption and relatively small errors. For the first time, this paper examines the application of unscented transformation (UT) technique, which is used in control and reliability engineering, to error propagation in the nuclear field for nonlinear cases. Using different examples, this paper shows that this deterministic method of UT produces better results compared to the conventional sandwich formula for error propagation. An example on error propagation given in the literature is revisited, and a calculation of the efficiency of a gamma-ray detector is also presented for illustrative purposes using the UT method.