不白之冤
injustice


不卑不亢
neither overbearing nor self-effecting
His manner with people is neither overbearing nor self-effecting.


不恥下問
learn from those beneath one
It's admirable that the old professor is willing to learn from those beneath him.


不計其數
countless


不假思索
without hesitation


不脛而走
spread like wildfire


不拘一格
not be limited to one type
When selecting staff you mustn't be limited to just one type.


不可救藥
be beyond help


不可思議
unblievable

不可一世
be insufferably arrogant

不了了之
leave unresolved
Since the suspect haven't been found, the case simply had to be left unresolved.


不謀而合
happen to coincide


不求甚解
Be content with a superficial understanding
He studies just to leave a superficial understanding

不三不四
1. （不正經）shady
2. （不象樣）neither one thing or the other

不速之客
uninvited guest
She was an uninvited guest at the party.
Yesterday evening we had an unexpected guest.

不同凡響
outstanding

不聞不問
be indifferent
He's indifferent to anything that doesn't have a bearing on him.

不相上下
be about the same


不修邊幅
scruffy

不學無術
ignorant and  incompetent
How can someone ignorant and incompetent be head teacher?


不遺餘力
do one's utmost
 The football team did its utmost to attract foreign football stars.


不翼而飛
disappear without trace


不約而同
happen to coincide
Everybody happened to vote in favor.

不擇手段
go to any lengths
He'll go to any length to get rich.


不擇不扣
He's a football fan through and through.


不知所措
be at loss


不自量力
overestimate one's abilities