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If the accessory doesn't show up as an pairing option, it may be because it's no longer in pairing mode. Sometimes the accessory will automatically turn off if it takes too long to pair with your iPhone. Try restarting the accessory and putting it back into pairing mode. If you can see the accessory as an option on your iPhone but can't get the accessory to work, you can make your iPhone "forget" the accessory so you can pair it again. To do this:  Open your iPhone's Settings. Tap Bluetooth. Tap the blue "i" in a circle next to the accessory's name. Tap Forget This Device. Tap the back button. Restart the accessory and put it into pairing mode. Select the accessory on your iPhone to pair with it. On the other hand, your iPhone may be the reason why you cannot pair with the Bluetooth device. Open the Control Center and tap the Bluetooth icon to turn Bluetooth off, and then again to turn it back on. If that doesn't help, try restarting your iPhone and then attempting to pair again. If you haven't updated your iPhone's operating system in a while, you may need to do so to use the accessory you're trying to pair with. Plug your iPhone into a power source, connect to Wi-Fi, and then check out How to Update iOS to proceed.
Restart the Bluetooth accessory. Unpair the Bluetooth device and reconnect. Restart Bluetooth on your iPhone. Upgrade to the latest version of iOS.