A Non-Intrusive Load Monitoring (NILM) method, robust even in the presence of unlearned or unknown appliances (UUAs) is presented in this paper. In the absence of such UUAs, this NILM algorithm is capable of accurately identifying each of the turned-ON appliances as well as their energy levels. However, when there is an UUA or set of UUAs are turned-ON during a particular time window, proposed NILM method detects their presence. This enables the operator to detect presence of anomalies or unlearned appliances in a household. This quality increases the reliability of the NILM strategy and makes it more robust compared to existing NILM methods. The proposed Robust NILM strategy (RNILM) works accurately with a single active power measurement taken at a low sampling rate as low as one sample per second. Here first, a unique set of features for each appliance was extracted through decomposing their active power signal traces into uncorrelated subspace components (SCs) via a high-resolution implementation of the Karhunen-Loeve (KLE). Next, in the appliance identification stage, through considering power levels of the SCs, the number of possible appliance combinations were rapidly reduced. Finally, through a Maximum a Posteriori (MAP) estimation, the turned-ON appliance combination and/or the presence of UUA was determined. The proposed RNILM method was validated using real data from two public databases: Reference Energy Disaggregation Dataset (REDD) and Tracebase. The presented results demonstrate the capability of the proposed RNILM method to identify, the turned-ON appliance combinations, their energy level disaggregation as well as the presence of UUAs accurately in real households.