Comment on trim string function please

Just looking for a few eyes on this code other than my own.

void TrimCString(char *str)
{
// Trim whitespace from beginning:
size_t i = 0;
size_t j;

while(isspace(str[i]))
{
i++;
}
if(i > 0)
{
for(j = 0; i < strlen(str); j++, i++)
{
str[j] = str[i];
}
str[j] = '\0';
}

// Trim whitespace from end:
i = strlen(str) - 1;

while(isspace(str[i]))
{
i--;
}
if(i < (strlen(str) - 1))
{
str[i + 1] = '\0';
}
}
.

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