When it comes to describing a lack of bias, there are many synonyms you can use besides "un-biasedly". Some options include impartially, evenhandedly, objectively, neutrally, fairly, equitably, justly, and open-mindedly. Each of these words carries a similar meaning to un-biasedly and can be used interchangeably in most contexts. For example, if you're describing a news outlet that reports information without any political leaning, you might say that they report the news impartially. Or, if you're describing a judge that doesn't take sides in a case, you might say that their decisions are made objectively. In any case, using these synonyms can help you communicate your message clearly without repeating the same word over and over.