#include<stdio.h>
main()
{
char *a="abcd";
char *b="cdef";
char c[10];
int i=0;
while(*a != *b)
{
c[i] = *a++;
i++;
}
while(*b != '\0')
{
c[i]= *b++;
i++;
}
printf("%s\n",c);
}

above code some thing wrong.
if "abcd","cefg" then output will be "abcdcefg"
but above code will give "abcefg"

Check the each char in the second string with first string
if it is not there then concatenate into the first string else
do not do.

char *strappend1(char *src,char *des)
{
 char *tmp=src;
 int f=0;
 while(*des)
 {
   while(*src!='\0')
   {
    if(*src==*des)
    {
     f=0;
     break;
    }
    else
      f=1;
    src++;
   }
  if(f==1)
  {
   *src++=*des;
   *src='\0';
  }
  des++;
 }
 return tmp;
}
int main(int argc,char **argv)
{
 char *src=argv[1],*des=argv[2];
 char *str;
 str=strappend1(src,des);
 printf("%s",str);
}

the code given by tarak is correct 

ie

#include<stdio.h>
main()
{
char *a="abcd";
char *b="cdef";
char c[10];
int i=0;
while(*a != *b)
{
c[i] = *a++;
i++;
}
while(*b != '\0')
{
c[i]= *b++;
i++;
}
printf("%s\n",c);
}

  

but the answer is abcdef and some garbage values yar 

abcdef{}>>>M<C<P{{  

to get perfect answer just add '\o' at end of the code and
before printf dear 




#include<stdio.h>
main()
{
char *a="abcd";
char *b="cdef";
char c[10];
int i=0;
while(*a != *b)
{
c[i] = *a++;
i++;
}
while(*b != '\0')
{
c[i]= *b++;
i++;
}

c[i]='\0';  //// new added line here






printf("%s\n",c);
}