The function takes a string input and transforms the first and third characters by incrementing the first character and decrementing the third character by 2 positions in the alphabet. The rest of the characters remain unchanged.

[CODE]:

```python
def transform_string(input_string):
    output_string = ""
    alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"

    for i, char in enumerate(input_string):
        if i == 0 or i == 2:
            if char in alphabet:
                new_index = (alphabet.index(char) + (2 * (-1) ** i)) % len(alphabet)
                output_string += alphabet[new_index]
            else:
                output_string += char
        else:
            output_string += char

    return output_string
```

Please confirm if this description and code match the function's behavior.