Do you have a replacement in mind for all diagram types of UML? The only modeling standards covering many diagrams of UML are the IDEF standards. But the IDEF notations lack tool support, even though it is much older than UML.
If you are looking for a substitute, you are not satisfied with UML ... since UML covers diagrams used at different stages of software development (requirements representation, software architecture and design, ...) you have to mention what diagram you want to find a substitute for.
UML is not a methodology, just a set of diagrams. RUP is the method/process associated with UML.
I have taught UML at university level for three years. As others have suggested, it will be very difficult to find a substitute for UML that covers the same broad spectrum of diagrams. Some alternatives are older, such as IDEF. Another alternative that comes to mind is something like Systems Modeling Language (SysML), which is actually an extension of and based on UML. This is also supported by IBM, and other companies that provide CASE software... I have met people who find certain UML diagrams (i.e. the more complex ones) difficult to learn... but I have not met anyone yet, who finds them unsatisfactory. Here are two links below related to SysML (recommended for modelling certain types of systems rather than being completely all-purpose). They can give you a quick idea in comparison with UML.
Object Process Methodology is an alternative. Taught in some CS courses including a couple at MIT.
Object process methodology (OPM) is an approach to designing information systems by depicting them using object models and process models. OPM was conceived and developed by Prof. Dov Dori, at the Technion – Israel Institute of Technology. A paper that first presented ideas underlying OPM was published in 1995. The comprehensive resource is Dori's book Object-Process Methodology – A Holistic Systems Paradigm.