When someone "takes no notice of" something, it means they are ignoring or disregarding it. In order to express this idea in different ways, there are a variety of synonyms to choose from. One option is to say that someone is "disregarding" or "overlooking" something. Alternatively, they could be "ignoring" or "brushing off" a particular issue. Another way to express not paying attention to something is to say that someone is "neglecting" it or "not acknowledging" it. It's important to choose the right synonym in order to convey the intended meaning and tone of a particular situation.