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A novel single-shot trapezoidal-gradient-based Lissajous trajectory is described and implemented on a 3-tesla magnetic resonance (MR) scanner. A feature of this trajectory is that its sampling points are located on a nonequidistant rectangular grid, which permits the usage of one-dimensional optimal algorithms to increase the robustness and speed of image reconstruction. Another advantage of the trajectory is that two images with different effective echo times can be obtained within a single excitation, which might be used for fast T2* mapping, in functional MR imaging scanning of brain activity associated with mental processes. Potential artifacts in reconstructed images were investigated and methods for suppressing these artifacts were developed. Experiments on normal subjects at rest and during brain activation were performed to demonstrate the feasibility of the new sequence.