'further annoyed' is a correct and usable phrase in written English.
It is an idiom, and it is typically used as an adjective phrase to signify that one's level of annoyance has increased. For example: Hearing her boss's rude comments further annoyed her.
Per then further annoyed them by bowing.
She further annoyed Ms. Brennan by placing many hires in a nonprofit group not covered by relevant decrees.
It also stopped sales commissions, which further annoyed suppliers, who rely on sales personnel to steer customers to higher-margin products.
His verbal misstep outraged serious runners, for whom race times are sacred — and Ryan further annoyed them with a lighthearted retraction this weekend.
The cop saw it there and it must have further annoyed him, but he studied the documents I handed him as if patiently mastering a difficult lesson.
He further annoyed tennis traditionalists by refusing to play at Wimbledon because of the event's dress code and the grass surfaces of its courts.
And Cuba will further annoy its powerful neighbour by having won far more golds, adjusted for GDP, than anyone else.
He then started Ola Toivonen, a promising new forward, in his first game against NAC last week, ahead of the incumbents, further annoying his detractors.
What's more, they might further annoy foreign governments already worried about the effect of a weaker yen on their own exporters.
The news - first reported by the British Journal of Photography - will further annoy British users of Adobe products, who have repeatedly vented frustration at the apparent disparity between prices of Adobe software in the US and UK.
So he agreed to meet 60 nurses privately two floors up, thereby further annoying most of the 478 who, just hours earlier, had supported a vote of no confidence in his policies.
