Residual magnetisation is one of the major sources of artefacts in single point imaging sequences with short repetition times. The unwanted signal is caused by non-dephased transverse magnetisation excited in preceding acquisition cycles. Therefore, the problem emerges mainly around the centre of k-space and has been solved in the past by additional spoiling gradients. In this work, unwanted residual magnetisation acquired with the SPRITE sequence was investigated and a new method for the suppression of residual magnetisation is presented. It is shown that residual magnetisation experiences a different phase encoding leading to residual images with a different FOV. A phase cycling filter is able to eliminate the unwanted signal. Furthermore, a description of all signal components that occur is presented using an operator notation. The notation is new in this field with respect to its completeness. That is, the signal description is based on an understanding of single point imaging sequences, such as SPRITE, by the use of an extended phase encode graph. A prominent in vivo example is that of sodium imaging in biological tissue where transverse relaxation times are such that unwanted coherences can occur and therefore residual magnetisation becomes a significant problem. For instance, sodium in biological tissue has two transverse relaxation times of approximately 3ms and 15ms at 4T and this can result in significant artefacts if the encoding time is short and TR<<3ms.