Is truncated hash collision resistant if original hash is collision resistant?

Let’s say I have a collision resistant hash function $H: {0,1}^* rightarrow {0,1}^n$ and I want to create another collision resistant hash function $H’: {0,1}^* rightarrow {0,1}^n$ using $H$ that leaks a bit of input. Would this still constitute a collision resistant hash function?

$$H'(xmathbinVert b) = H(x)_{[1ldots n-1]} mathbin| b$$

(Here, $b$ is a single bit)