How to simultaneously update 2 services with kubernetes without downtime?

Kubernetes rolling updates will be creating new pods with updates and gradually change old pods by new, and as soon as new pod is ready it will get traffic by round-robin with the old ones.

But what to do in case that I have 2 services one is using another and I need to make updates in them simultaneously? I don’t want the situation that old service 1 will make calls to new service 2.