Bing [1] constructed a compactum $X$ in $\mathbb R^3$ which has the fixed point property but $X\cup D$ does not, where $D$ is a rectangle and $X\cap D$ is an interval. He also asked whether $X\times [0,1]$ has the fixed point property. In [4] Young gave a positive answer to this question. The aim of this note is to extend Young's result to the product $X\times A$ where $A$ is a compact AR-space. The result does not hold if $A$ is a compact fixed point space.