The trick here is to use the non-eager version of * (code not tested):

s/
  <  # match '<'
  .*? # match anything, but as short as possible
  (\{|$) # match either '{' or end of line
//x
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The format of the file contains Ascii characters. When I try to print the line,it only prints till EVITE LA ENFERMEDAD PERIODONTAL<. Please tell me any way we can encode the file

#!/usr/bin/perl
while(<DATA>){
$_ =~ s/<.*?(\{|$)//x;
print $_;
}

__DATA__
EVITE LA ENFERMEDAD PERIODONTAL<                   AS
{IT}CTIQUE LA HIGIENE DENTAL PARA CUIDAR SUS ENCÃ   Cuando hace casi d
+os años visité a mi dentista para hacerme un chequeo
dental , me encontré ante un problema que podía terminar con mi dent
+adura.
Siempre tuve unos dientes sanos y jamás se me ocurrió pensar que pod
+ía  perder
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The format of the file contains Ascii characters.

??? I think you mean "contains non-ascii characters".

it only prints till EVITE LA ENFERMEDAD PERIODONTAL<

Are you sure that it also prints the '<' less sign? With the code you have posted, the '<' should not be printed. At least it does not for me:

$ perl -lwe 'my $_="EVITE LA ENFERMEDAD PERIODONTAL<    AS"; s/<.*?(\{
+|$)//; pr
int'
EVITE LA ENFERMEDAD PERIODONTAL
[download]

Please tell me any way we can encode the file

I'm not sure what you mean by "encode the file". Maybe you find what you need in perlio, where the encoding layer is described.
-- 
Ronald Fischer <ynnor@mm.st>

#!/usr/bin/perl

use strict;

my $count = 0;
while( <DATA> ) {
    $count = 1 if ( /\</ );
    $count = 0 if ( /^{/ );
    print if ( $count == 0 );
}


__DATA__
hello
 EVITE LA ENFERMEDAD PERIODONTAL<
EVITE LA ENFERMEDAD PERIODONTAL<                   AS
{IT}CTIQUE LA HIGIENE DENTAL PARA CUIDAR SUS ENCÃ
test
test
[download]

$_ =~ m/\{/g;
$str = $`;
$str1=$';
$str=~ s/\>//g;

print $str."{".$str1;
[download]

Not really.

If there is a line in the input data that has neither a > or a { it will produce a wrong result.

use strict;
use warnings;

while (<DATA>) {
    $_ =~ m/\{/g;
    my $str = $`;
    my $str1=$';
    $str=~ s/\>//g;

    print $str."{".$str1;
}
__DATA__
testline1
 EVITE LA ENFERMEDAD PERIODONTAL<
EVITE LA ENFERMEDAD PERIODONTAL<                   AS
{IT}CTIQUE LA HIGIENE DENTAL PARA CUIDAR SUS ENCÃ
testline2
testline3
[download]

produces the output

Use of uninitialized value in substitution (s///) at ...
Use of uninitialized value in concatenation (.) or string at ...
    <snip other warnings>
{{{{IT}CTIQUE LA HIGIENE DENTAL PARA CUIDAR SUS ENCÃ
    <snip more warnings>
{IT}CTIQUE LA HIGIENE DENTAL PARA CUIDAR SUS ENCÃ
    <snip more warnings>
{IT}CTIQUE LA HIGIENE DENTAL PARA CUIDAR SUS ENCÃ
[download]

cheers, si_lence

I apologize for the lack of exclamation marks in this post