If you describe someone as a straight arrow, you mean that they are very conventional, honest, and moral. I was very much a product of my environment. I was very traditional, a real straight arrow in lots of ways. Several friends describe Mr. Menendez as `a straight arrow' who rarely drank and was close to his family. Note: You can use straight-arrow before a noun. It was impossible to imagine such a well-scrubbed, straight-arrow group of young people rioting over anything.