The PRESTO sequence is a well-known 3-D fMRI imaging sequence. In this sequence the echo planar imaging technique is merged with the echo-shift technique. This combination results in a very fast image acquisition, which is required for fMRI examinations of neural activation in the human brain. The aim of this work was to use the basic Cartesian PRESTO sequence as a framework when developing a novel trajectory using a non-Cartesian grid. Our new pulse sequence, PRESTO CAN, rotates the k-space profiles around the ky-axis in a non-Cartesian manner. This results in a high sampling density close to the centre of the k-space, and at the same time it provides sparser data collection of the part of the k-space that contains less useful information. This "can- or cylinder-like" pattern is expected to result in a much faster k-space acquisition without loosing important spatial information. A new reconstruction algorithm was also developed. The purpose was to be able to construct an image volume from data obtained using the novel PRESTO CAN sequence. This reconstruction algorithm was based on the gridding technique, and a Kaiser-Bessel window was also used in order to re-sample the data onto a Cartesian grid. This was required to make 3-D Fourier transformation possible. In addition, simulations were also performed in order to verify the function of the reconstruction algorithm. Furthermore, in vitro tests showed that the development of the PRESTO CAN sequence and the corresponding reconstruction algorithm were highly successful. In the future, the results can relatively easily be extended and generalized for in vivo investigations. In addition, there are numerous exciting possibilities for extending the basic techniques described in this thesis