The financial cost of missed appointments is so great that even a small percentage reduction in Did Not Attend (DNA) rate could save significant sums of money. Previous studies have identified many factors that predict DNA rate, including patient age, gender, and transport options. However, it is not obvious how healthcare providers can use this information to improve attendance, as such factors are not under their control. One factor that is under administrative control is appointment scheduling. Here we asked whether DNA rate could be reduced by altering scheduling policy. In Study 1, we examined attendance records for 4,538,294 outpatient hospital appointments across Scotland between January 1st 2008 and December 31st 2010. DNA rate was highest for Mondays (11%), lowest for Fridays (9.7%), and decreased monotonically over the week (Monday-Friday comparison [χ(2)(1, N = 1,585,545) = 722.33, p<0.0001]; Relative Risk Reduction 11.8%). This weekly decline was present for male and female patient groups of all ages, but was steeper for younger age groups. In Study 2, we examined attendance records for 10,895 appointments at a single GP clinic in Glasgow. Here again, DNA rate was highest for Mondays (6.2%), lowest for Fridays (4.2%), and decreased monotonically over the week (Monday-Friday comparison [χ(2)(1, N = 4767) = 9.20, p<0.01]; Relative Risk Reduction 32.3%). In two very different settings, appointments at the beginning of the week were more likely to be missed than appointments at the end of the week. We suggest that DNA rate could be significantly reduced by preferentially loading appointments onto high-attendance days.