How to redirect the output of the time command to a file in Linux?

Just a little question about timing programs on Linux: the time command allows to
measure the execution time of a program:

[ed@lbox200 ~]$ time sleep 1

real    0m1.004s
user    0m0.000s
sys     0m0.004s

Which works fine. But if I try to redirect the output to a file, it fails.

[ed@lbox200 ~]$ time sleep 1 > time.txt

real    0m1.004s
user    0m0.001s
sys     0m0.004s

[ed@lbox200 ~]$ cat time.txt 
[ed@lbox200 ~]$ 

I know there are other implementations of time with the option -o to write a file but
my question is about the command without those options.

Any suggestions ?