The term has a special meaning in 4th Way parlance. Even there, the word is used in two somewhat different meanings:

Firstly, negative emotion refers to what is generally called negative emotion, such as anger, fear, jealousy, envy etc.

Secondly, specially with the QFS, the word is also used to indicate an emotion that does not accord with objective reality. This has nothing to do with whether the emotion is perceived as agreeable or not. Feeling happy as a result of self-calming or deliberately inducing oneself to believe in an illusion as an example of negative emotion in this sense.

Non-expression of negative emotions is an important precept of the 4th Way. This does not mean that these should be ignored, quite the opposite. However, the energy of these emotions should not be wasted in mechanically expressing these but should rather be transformed and kept within the organism. This offers an opportunity for self-knowledge and saves energy which is then available for transformation.

Ouspensky and Mouravieff discuss negative emotions somewhat differently. They however agree that shocks, which often take the form of disagreeable emotion are an essential element of the Work. The central concept is consciously catching the automatic, mechanical reaction to the shock before the 'human machine' starts 'running' its habitual 'program.' The program itself may be to respond with anger, fear, denial or any other humanly possible response. In the place of doing this, the student may be deeply cognizant of the situation and of the program response and decide not to react in the habitual way. Because situations and habitual responses vary, we cannot give universally valid definitions of particulars.

A transformed negative emotion, according to Ouspensky, does not become a 'positive emotion' in the sense of being made from unpleasant to pleasant. Rather, it transforms into a deeper understanding that transcends the pleasant/unpleasant judgement typical to mechanical thinking and feeling. In 4th Way theory, the coarser 'hydrogen' of mechanically received impressions has been transformed into a finer one, which can act as fuel for the higher centers.

See Hydrogen, Self-Remembering, In Search of the Miraculous, Gnosis.