davido has the best idea but if you want to use a regex you can use something like:

my $list = 
"RcvChar
checkeof
SerialOutputString
SerialOutputString
SerialOutputString
GetFile
ChksumByteByByte
GetChksum
SerialOutputString
SerialOutputString";
while ($list =~ s/(\b\w+\b)(.*?)\s+\1\b/$1$2/s) {};
print $list;
[download]

outputs :

RcvChar
checkeof
SerialOutputString
GetFile
ChksumByteByByte
GetChksum
[download]