The phrase "avoid the suspicion" is correct and usable in written English.
You can use it when discussing actions taken to prevent others from doubting or questioning someone's motives or behavior.
Example: "To maintain a good reputation, it is essential to avoid the suspicion of wrongdoing in all business dealings."
Alternatives: "elude the doubt" or "prevent the mistrust".
It is hard to avoid the suspicion, nevertheless, that Hasler and Manly fancy their chances.
And it's hard to avoid the suspicion that big contributions from Wall Street helped grease the rails.
It becomes difficult to avoid the suspicion that actually it is the "have-nots" the government is seeking to target.
In fact, it's hard to avoid the suspicion that G.O.P. leaders actually want the economy to perform badly.
It's hard to avoid the suspicion that, in at least some cases, surprise medical bills are a deliberate moneymaking strategy.
But it is hard to avoid the suspicion that in retiring with Kevin Pietersen's international future unresolved, Strauss has handed his successor, Alastair Cook, a classic hospital pass.
Marijuana business owners have devised strategies to avoid the suspicions of bankers.
And although none of its riders have ever failed a drug test, the Discovery team was not able to avoid the suspicions of doping that have beset the sport.
On Election Night, computers can usually produce the final results faster than any other method of tabulation, and so enable local officials to please reporters on deadlines and to avoid the suspicions of fraud which long delays in counting can stimulate.
Forbes: So if we have the centralized clearing, we'll avoid the suspicions of phony CDS transactions to put pressure on stocks, or make rating agencies think that, "Oh, maybe the bonds aren't what we thought they were," and start all of that?
Kneeling on the mountains of paper, flashlights in our mouths, the atmosphere sweltering and soggy under the closed bin covers (which we had shut to avoid the suspicions of nosy neighbors), we scanned the discarded recyclables of the residents of Oak Forest, Illinois.
