[R-sig-ME] Meaning of perfect correlation between by-intercept and by-slope adjustments

[Petar Milin]

Hello!
Simplified model that I have is:
lmer(Y ~ F1 + F2 + C1 + (1+F1|participants) + (1|items))
F1 and F2 are categorical predictors (factors) and C1 is a covariable 
(continuous predictor). F1 has five levels.
By-participant adjustments for F1 are justified (likelihood ratio test 
is highly significant). However, what puzzles me is perfect correlation 
between two levels of F1. Others are quite high, but not perfect. I 
wonder what this means, exactly? Is there some "lack of information" 
which leads to problems in estimating variances?

Thanks!
Petar