Unemployment Insurance Improvement Act This bill expands the list of requirements a state unemployment compensation system must follow to be compliant under federal law. Specifically, the bill requires the maximum benefit period available to an individual be at least 26 weeks. The base period used to determine unemployment eligibility must consist of at least four completed calendar quarters preceding the claim and must include the most recently completed calendar quarter. Further, compensation must not be denied to an otherwise eligible individual who earns at least $1,000 during the highest quarter and at least $1,500 during the entire base period. Finally, compensation must not be denied under an ability to work, active search for work, or refusal to accept work provision solely on the basis of the number of hours of work the individual is seeking, so long as the individual is seeking at least 20 hours of work or half the hours the individual typically worked. Employers that pay unemployment taxes to a noncompliant state system cannot claim amounts paid into the state system as a credit against federal unemployment tax due. The bill also requires states to meet specified online claim system accessibility requirements and to ensure that offline means of filing are available. A state that does not comply cannot receive federal funds for administration of its state unemployment system.