This was one of many writing techniques rules I learned a few years ago.
Why should writers avoid putting statements in the negative form? According to KwizNet’s website, putting statements in the affirmative form “tells or asks about what is.” It is important to tell readers what they want or need to know, not what they don’t. Therefore, when writing, think about replacing negative words or ideas with affirmative ones. Here are some examples:
dishonest instead of not honest
ignored instead of did not pay attention to
By using affirmative structures, you make clearer, more definite assertions. As a side note, not is to be used as a means of denial or antithesis.
Instead of writing:
He was not very often on time.
Lisa did not remember to file her income tax report this year.
He usually came late. (My italics.)
Lisa forgot to file her income tax report this year.
Notice how the above sentences are more concise when cast in an affirmative light.
If writers are to avoid negative structures, so too should translators. Certain languages such as French tend to use many negative forms in writing.
N’oubliez pas de poser votre candidature avant le 30 novembre prochain.
En écoutant sa jolie voix, je n’avais qu’une seule envie, rentrer chez moi dans mon île.
In translation, it is generally advisable to avoid “Don’t forget,” “it is not,” and so on. Consider affirmative equivalents such as
Remember to apply before November 30.
Listening to her lovely voice, I longed for home and my island.
Like writing, affirmative structures in translation make sentences more concise. Because sentences are more concise, they are shorter in length. As a general rule, English texts and translations are shorter than their French counterparts.
 “Grammar, Punctuation, and Style: 3.5 Put Statements in Positive Form.” Publishing date unknown. Kwiznet Learning System. Kwiznet. Web. 29 September 2014. Path: Statements; Negative Form <http://www.kwiznet.com/p/takeQuiz.php?ChapterID=12263&CurriculumID=58&Num=3.5>.
 Jean Delisle, La traduction raisonnée : Manuel d’initiation à la traduction professionnelle de l’anglais vers le français, 2e édition. Les Presses de l’Université d’Ottawa, 2003, 415.
 Ibid, 415 (original English text). Possible back translation: “By listening to her lovely voice, I wanted to return home to my island.”