Strange problem with daisy chained shift registers

I connected 2 74HC595 shift register ICs together in a daisy chain and encountered a very annoying effect. I searched the internet quite long for the solution and there is no mention of it anywhere.

The setup

2 x 74HC595 daisy chained
16 x LED with resistor
1 x Arduino UNO

Scenario #1

I turn on the LEDs one by one from 0 to 15. --- > It works perfectly.
I turn off the LEDs one by one from 0 to 15. --- > When i turn off the number 0 it also turns off the number 8. When i turn off the number 1 it turns the number 8 back on. The rest of the sequence is fine.

Scenario #2

I turn off all the LEDs and turn on number [ i+8 ]. After that i blink number [ i ]. --- > It works perfectly.
I turn on all the LEDs and start blinking the number [ i ] . --- > Number [ i+8 ] also blinks.

I tested it with several codes found on the internet and shows the same effect every time.
I tested it with the ShiftOut tutorial.
I tested it with advanced shiftout without the 8 bit restriction problem.
I tested it with delay and without delay functions.
All the same problem.

Something is wrong with either your program or your circuit, neither of which you have posted

Please post both