The function takes a string as an input and increments the alphabetical letters by 20 positions. If the letter reaches the end of the alphabet ('z' for lowercase, 'Z' for uppercase), it wraps around to the beginning of the alphabet and continues incrementing. Non-alphabetic characters remain unchanged.

[CODE]: 
```python
def increment_letters(input_string):
    output = ""
    for char in input_string:
        if char.isalpha():
            if char.islower():
                output += chr(((ord(char) - ord('a') + 20) % 26) + ord('a'))
            elif char.isupper():
                output += chr(((ord(char) - ord('A') + 20) % 26) + ord('A'))
        else:
            output += char

    return output
```