Try,
Ex: What should I do so that this message is not displayed?
Ex: What should I do so that this message does not display (on its own)? 

Originally Posted by
Tvita
The point was that I just want to learn a new structure.
OK. No worries. The structure that you're asking about is called a negated infinitive. Like these examples:
negated to-infinitive: not to do
negated bare infinitive: to not do
You can use either structure, but be sure you know the basics before you go ahead and do so. 
Not is a negative adverb and to do is an infinitive verb. There are two kinds of infinitives, those that take the to-particle and those that don't:
to-infinitive: to do (e.g., They want to do the homework.)
bare infinitive: do (e.g. Watch them do the homework.)
Now, to negate those examples sentences the adverb not is added before the verb you want to negate. Like this,
1. They do not want to do the homework.
2. Watch them not do the homework.
Notice the form not do in 2. occurs naturally in the grammar, because it is for that very reason that speakers and writers split to-infinitives here:
Ex: What should I do to not see this message? <split>
Ex: What should I do not to see this message?
Both of those examples reflect native-speaker English; however, traditionalists' views, which many exams questions are based on, feel that since to see is entire verb, the adverb not shouldn't come between it:
Traditionalists
What should I do to not see this message? 
What should I do not to see this message? 
Now, non-traditionalists, also called descriptivists, look at how speakers use language, and so when they see speakers splitting to-infinitives, they don't say it's ungrammatical or unacceptable or wrong, they ask why speakers are doing it. According to descriptivists, speakers split infinitives because the to-particle carries no meaning, and so the closer an adverb is to the word it modifes, the more powerful the modification will be. Which is why some, if not most native speakers will tell you that the first example--the one prescriptivists find ungrammatical--sounds better than the second example:
Descriptivists
What should I do to not see this message? 
What should I do not to see this message?